## determinants question bank

06/12/2020 Uncategorized

Free Question Bank for JEE Main & Advanced Mathematics Determinants & Matrices Self Evaluation Test - Determinats This article covers the matrices and their types, operations on matrices, transpose of a matrix, adjoint of a matrix, determinant of a matrix, the inverse of a matrix, cofactors of a matrix, to find the solution for a system of equations through matrix method, types of solutions and cube roots of unity. The price of good B. Previous Years Examination Questions 1 Mark Questions 4 Mark Questions. Question 4: ∣ 1aa2−bc1bb2−ac1cc2−ab ∣=\left| \,\begin{matrix} 1 & a & {{a}^{2}}-bc \\ 1 & b & {{b}^{2}}-ac \\ 1 & c & {{c}^{2}}-ab \\ \end{matrix}\, \right|=∣∣∣∣∣∣∣​111​abc​a2−bcb2−acc2−ab​∣∣∣∣∣∣∣​= _________. Matrices and Determinants carry a total of 12-13 marks in the CBSE Class XII Board Examination. For example, poor management can be the source of a weak loan portfolio or sloppy supervision, and regulatory forbearance can make conditions ripe for rogue traders and fraud. Access the answers to hundreds of Determinant questions that are explained in a way that's easy for you to understand. Aburime suggested that the bank level of safety achieved through the high capital requirements which generated positive net benefits. Matrices and Determinants 9.1 Introduction: In many economic analysis, variables are assumed to be related by sets of linear equations. Consistency, inconsistency and â¦ To avail this offer call us at 9212462845 At x = −1, ∣ 14201−251−25 ∣ =0\left| \,\begin{matrix} 1 & 4 & 20 \\ 1 & -2 & 5 \\ 1 & -2 & 5 \\ \end{matrix}\, \right|\,=0∣∣∣∣∣∣∣​111​4−2−2​2055​∣∣∣∣∣∣∣​=0 as R2 = R3. Bankâs capital is widely used as one of the determinants of bank profitability since it indicates the financial strength of the bank (Athanasoglo et al., p. 14). This poses generalizability questions without further replications and validations. 3. Important questions for Class 12 Maths Chapter 4 determinants are given here. Students can solve NCERT Class 12 Maths Determinants MCQs Pdf with Answers to know their preparation level. Matrix algebra provides a clear and concise notation for the formulation and solution of such problems, many of which would be â¦ To avail this offer call us at 9212462845, Attention Class XII standard Aspirants! These questions include all the important topics and formulae. Different types of factors are covered on the quiz. adjoint and inverse of a square matrix. December Offer : Online Exam Software Starts @ Rs.5000/- only. The population of study was all the 44 commercial bank licensed to operate in Kenya as at 31st December 2013. Question 2: If P=[3212−1232], A=[1101] P=\left[ \begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \\ \end{matrix} \right],\,A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]P=[23​​−21​​21​23​​​],A=[10​11​] and Q = PAPT, then P (Q2005)PT equal to ________. Students can practice these problems for the board examinations. 2. Question 12: If ∣ x2+xx+1x−22x2+3x−13x3x−3x2+2x+32x−12x−1 ∣=Ax−12,\left| \,\begin{matrix} {{x}^{2}}+x & x+1 & x-2 \\ 2{{x}^{2}}+3x-1 & 3x & 3x-3 \\ {{x}^{2}}+2x+3 & 2x-1 & 2x-1 \\ \end{matrix}\, \right|=Ax-12,∣∣∣∣∣∣∣​x2+x2x2+3x−1x2+2x+3​x+13x2x−1​x−23x−32x−1​∣∣∣∣∣∣∣​=Ax−12, then what is the value of A? 12th Mathematics chapter 4 Determinants have many topics. These questions include all the important topics and formulae. Get The Complete Question Bank Splitting the determinant into two determinants, we get. JEE Main Maths Matrices And Determinants Previous Year Questions With Solutions. Important questions, guess papers, most expected questions and best questions from 12th Mathematics chapter 4 Determinants have CBSE chapter wise important questions with solution for free download in PDF format. Important Questions for Class 12 Maths Class 12 Maths NCERT Solutions Home Page The question papers and CBSE with Determinants practice papers for 12 Mathematics, Determinants are very helpful for students who wish to get good marks in exams. If a patient has trouble getting rides to her doctor, you might wonder why there are no bus lines in her community. The worksheet and quiz give you the ability to assess your understanding of health determinants. Define Velocity Of Money And Discuss The Major Determinants Of Velocity. Practice JEE Main Important Topics Questions solved by our expert teachers helps to score good marks in IIT JEE Exams. (C1 → C1 + C2 + C3) (Because 1 + ω + ω2 = 0). Question: 1. The price of labour used in the production of good C. The amount of technology used in the production of good D. The cost of the plant used to produce good Answer: A X X X X Difficulty: Easy [QUESTION] As the price of a good rises: Question 9: If a, b, c are unequal what is the condition that the value of the following determinant is zero Δ=∣ aa2a3+1bb2b3+1cc2c3+1 ∣\Delta =\left| \,\begin{matrix} a & {{a}^{2}} & {{a}^{3}}+1 \\ b & {{b}^{2}} & {{b}^{3}}+1 \\ c & {{c}^{2}} & {{c}^{3}}+1 \\ \end{matrix}\, \right|Δ=∣∣∣∣∣∣∣​abc​a2b2c2​a3+1b3+1c3+1​∣∣∣∣∣∣∣​? The list of causes as they appear below is for ease of exposition â it is rare to find a single cause for bank failure; rather, there are a number of contributing factors. Question 8: If – 9 is a root of the equation ∣ x372x276x ∣=0\left| \,\begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{matrix}\, \right|=0∣∣∣∣∣∣∣​x27​3x6​72x​∣∣∣∣∣∣∣​=0 = 0, then the other two roots are ________. Test your knowledge of the Social Determinants of Health (SDOH) with the questions below â place your mouse cursor over a card to reveal a Fact or Fiction statement and click on the âAnswerâ button to learn more. Also, additional important questions are also provided here. Dear User, Kindly login/register to view answer & explanation of each question. Quiz & Worksheet Goals Then the value of the determinant ∣ 1111−1−ω2ω21ω2ω4 ∣\left| \,\begin{matrix} 1 & 1 & 1 \\ 1 & -1-{{\omega }^{2}} & {{\omega }^{2}} \\ 1 & {{\omega }^{2}} & {{\omega }^{4}} \\ \end{matrix}\, \right|∣∣∣∣∣∣∣​111​1−1−ω2ω2​1ω2ω4​∣∣∣∣∣∣∣​ is ______. =>−2{−c2(b2a2)+b2(−c2a2)}=4a2b2c2-2\{-{{c}^{2}}({{b}^{2}}{{a}^{2}})+{{b}^{2}}(-{{c}^{2}}{{a}^{2}})\}=4{{a}^{2}}{{b}^{2}}{{c}^{2}}−2{−c2(b2a2)+b2(−c2a2)}=4a2b2c2. CBSE Latest Practice Papers. The important discussions in Determinants are as follows: Some example questions from this chapter are given here. The determinant will be ∣ 234345567 ∣=0\left| \,\begin{matrix} 2 & 3 & 4 \\ 3 & 4 & 5 \\ 5 & 6 & 7 \\ \end{matrix}\, \right|=0∣∣∣∣∣∣∣​235​346​457​∣∣∣∣∣∣∣​=0. Questions are expected in the various sections of the question paper corresponding to (i) Very Short Answer Type (VSA) Questions: 1 Mark, (ii) Short Answer Type (SA) Questions: 2 Marks, (iii) Long Answer Type I (LA-I) Questions: 4 Marks, and Because a, b, c are different, the second factor cannot be zero. A−1=16(A2+cA+dI)A^{-1}=\frac{1}{6}(A^{2}+cA+dI)A−1=61​(A2+cA+dI) where c, d ∈ R, then pair of values (c, d) are __________. Assume GDP Is Currently $10,850 Billion Per Year And The Quantity Of Money Is$833 Billion. The research methodology adopted by the study was descriptive research design. However I find there is multicollinearity among the macroeconomic factors in US economy. The Nation Collectively Holds Enough Money To Finance How Many Days Worth Of GDP Expenditure? Question 5: The roots of the equation ∣ 14201−2512x5x2 ∣=0\left| \,\begin{matrix} 1 & 4 & 20 \\ 1 & -2 & 5 \\ 1 & 2x & 5{{x}^{2}} \\ \end{matrix}\, \right|=0∣∣∣∣∣∣∣​111​4−22x​2055x2​∣∣∣∣∣∣∣​=0 = 0 are _________. Question 10: If pλ4+qλ3+rλ2+sλ+t=∣ λ2+3λλ−1λ+3λ+12−λλ−4λ−3λ+43λ ∣,p{{\lambda }^{4}}+q{{\lambda }^{3}}+r{{\lambda }^{2}}+s\lambda +t=\left| \,\begin{matrix} {{\lambda }^{2}}+3\lambda & \lambda -1 & \lambda +3 \\ \lambda +1 & 2-\lambda & \lambda -4 \\ \lambda -3 & \lambda +4 & 3\lambda \\ \end{matrix}\, \right|,pλ4+qλ3+rλ2+sλ+t=∣∣∣∣∣∣∣​λ2+3λλ+1λ−3​λ−12−λλ+4​λ+3λ−43λ​∣∣∣∣∣∣∣​, then the value of t is ______. These questions cover several short answer type questions, long answer type questions that are crucial for CBSE class 12 exams. In the NCERT Solutions for Class 12 Maths Chapter 4 Determinants, the focus is on the properties of determinants that simplifies its evaluation by obtaining the maximum number of â¦ 2. If you want to join our unlimited test series, then please write us at, We provide you the most simplest and user friendly web portal to conduct, Conduct online exam/test, without internet and update it as per internet/electricity availability within 3 days, Copyright Â© 2020,  All right reserved  |  A Unit of. Chapter Wise Important Questions Class 12 Mathematics. JEE Maths Question Bank for Matrices: The students who are appearing for Joint Entrance Examination (JEE) can check the JEE Maths Question Bank for Matrices from this page.This question bank covers a wide range of questions so that â¦ October Offer : Online Exam Software Starts @ Rs.5000/- only. Question 1: Question 14: Let ω=−12+i32\omega =-\frac{1}{2}+i\frac{\sqrt{3}}{2}ω=−21​+i23​​. The last research question was; what are the macroeconomic which influence the financial performance of the commercial banks? Here we have covered Important Questions on Determinants for Class 12 Maths subject.. Maths Important Questions Class 12 are given below.. Short Answer Type Questions For infinitely many solutions, the two equations must be identical. Since it is an identity in ∣ a(1+w)bw2awb(w+w2)cbw2c(w2+1)awc ∣\left| \,\begin{matrix} a(1+w) & b{{w}^{2}} & aw \\ b(w+{{w}^{2}}) & c & b{{w}^{2}} \\ c({{w}^{2}}+1) & aw & c \\ \end{matrix}\, \right|∣∣∣∣∣∣∣​a(1+w)b(w+w2)c(w2+1)​bw2caw​awbw2c​∣∣∣∣∣∣∣​, Now put BC = [−b  −a] [-b\,\,-a]\,[−b−a] (a−a)\begin{pmatrix} a\\ -a \end{pmatrix}(a−a​), = [a2 −ab] in the given equation, we have, Question 11: The determinant ∣ abaα+bbcbα+caα+bbα+c0 ∣=0\left| \,\begin{matrix} a & b & a\alpha +b \\ b & c & b\alpha +c \\ a\alpha +b & b\alpha +c & 0 \\ \end{matrix}\, \right|=0∣∣∣∣∣∣∣​abaα+b​bcbα+c​aα+bbα+c0​∣∣∣∣∣∣∣​=0 if a, b, c are in, = a {−c(aα2+2bα+c)−0}−b{−b(aα2+2bα+c)−0} by expanding along. Trick: Obviously by inspection, x = −1, 2 satisfy the equation. By solving JEE Main January 2019 chapterwise questions with solutions will help you to score more in your IIT JEE examination. Staikouras 2008) consider the external determinants of the bankâs profitability, such as GDP growth rate, federal discount rate and inflation. Determinants Important Questions for CBSE Class 12 Maths Properties of Determinants. Free PDF Download of JEE Main Matrices and Determinants Important Questions of key topics. Question 15: The number of values of k for which the system of equations (k + 1) x + 8y = 4k, kx + (k + 3) y = 3k − 1 has infinitely many solutions, is _______. ⇒ (x + 9) {(x2 − 12) − (2x − 14) + (12 − 7x)} = 0. Try this amazing Determinants Of Health quiz which has been attempted 3252 times by avid quiz takers. About 2-3 questions are asked from this topic in JEE Examination. 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2 January 8, 2020 by Prasanna Students can Download Maths Chapter 4 Determinants Ex 4.2 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. [QUESTION] Which one of the following determinants will cause movements along the supply curve of good X? ⇒ [k + 1] / [k] = [8] / [k + 3] = [4k] / [3k − 1], ⇒ (k + 1) (k + 3) = 8k and 8 (3k − 1) = 4k (k + 3), Matrices And Determinants Previous Year Questions With Solutions. Exercise 4.1 â 8 Questions (3 Short Questions and 5 Long Questions) 4.3 Properties of Determinants. In this study, I only use Federal Reserve Bank Discount Rate as a measure of macroeconomic activity. Determinants (20 Periods) Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Therefore, by A−1=16(A2+cA+dI)A^{-1}=\frac{1}{6}(A^2+cA+dI)A−1=61​(A2+cA+dI), ⇒ 6 = 1 + c + d, (by equality of matrices). with value â1. Also explore over 61 similar quizzes in this category. Just Exam provide a platform to all students who want to make practice for various subject online. Download JEE Main 2019 (Jan) Chapter wise solved questions for mathematics in PDF format prepared by expert IIT JEE Teachers at Mathongo.com. All worksheets have been carefully compiled for all level of students, you can also download in PDF CBSE Class 12 Determinants Chapter wise question bank and use them for further studies. Carefully understand the syllabus for Class 12 Determinants and download the worksheets for the topics which you have studied today. In other words, there are social determinants of health care, social determinants of health, and social determinants of health equity. Students can Download Basic Maths Question Bank Chapter 1 Matrices and Determinants Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board â¦ Here you can get Class 12 Important Questions Maths based on NCERT Text book for Class XII.Maths Class 12 Important Questions are very helpful to score high marks in board exams. Questions about transportation may lead to asking about equity. Determinant. In Uttar Pradesh State Entrance Examination (UPSEE), the chapter Matrices and Determinants play an important role. or aα2+2bα+c=0. We prepare this platform on the base of CBSE. Question 6: ∣ a+ba+2ba+3ba+2ba+3ba+4ba+4ba+5ba+6b ∣=\left| \,\begin{matrix} a+b & a+2b & a+3b \\ a+2b & a+3b & a+4b \\ a+4b & a+5b & a+6b \\ \end{matrix}\, \right|=∣∣∣∣∣∣∣​a+ba+2ba+4b​a+2ba+3ba+5b​a+3ba+4ba+6b​∣∣∣∣∣∣∣​= __________. because few maths chapters are numerical based theoretical based, and few IQ based thats why doing not well. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 4 Determinants. Thus, Δ=0, if either b2−ac=0or aα2+2bα+c=0 i.e., a,b,c in G.P. Get help with your Determinant homework. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. where c, d ∈ R, then pair of values (c, d) are __________. About 2-3 questions are asked from this topic in JEE Examination. A. A2005 = [1200501]\left[ \begin{matrix} 1 & 2005 \\ 0 & 1 \\ \end{matrix} \right][10​20051​], Question 3: If A=[α011]and B=[1051]A=\left[ \begin{matrix} \alpha & 0 \\ 1 & 1 \\ \end{matrix} \right] and \ B=\left[ \begin{matrix} 1 & 0 \\ 5 & 1 \\ \end{matrix} \right]A=[α1​01​]and B=[15​01​] then value of α for which A2 = B, is. What Is The Velocity Of Money? For example Mathematics Matrices and Determinants chapter, After differential chapter reading, we want do all examples of differential chapter and NCERT, illustrations, practice paper, question paper, jee mains, practice problems, Sample papers, Model Test Paper, Solved Practice â¦ Question 7: ∣ b2+c2a2a2b2c2+a2b2c2c2a2+b2 ∣=\left| \,\begin{matrix} {{b}^{2}}+{{c}^{2}} & {{a}^{2}} & {{a}^{2}} \\ {{b}^{2}} & {{c}^{2}}+{{a}^{2}} & {{b}^{2}} \\ {{c}^{2}} & {{c}^{2}} & {{a}^{2}}+{{b}^{2}} \\ \end{matrix}\, \right|=∣∣∣∣∣∣∣​b2+c2b2c2​a2c2+a2c2​a2b2a2+b2​∣∣∣∣∣∣∣​= _________. Fact orâ¦ Question 13: Let ∣ 6i−3i143i−1203i ∣=x+iy,\left| \,\begin{matrix} 6i & -3i & 1 \\ 4 & 3i & -1 \\ 20 & 3 & i \\ \end{matrix}\, \right|=x+iy,∣∣∣∣∣∣∣​6i420​−3i3i3​1−1i​∣∣∣∣∣∣∣​=x+iy, then, => [6i(-3 + 3) + 3i(4i + 20) + 1(12 – 60i) = x + iy. 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Solved by our expert teachers helps to score more in your IIT JEE Examination Offer call us 9212462845. Starts @ Rs.5000/- only why doing not well Kenya as at 31st December 2013 10,850... & worksheet Goals free PDF Download was Prepared based on Latest Exam Pattern = −1, 2 satisfy the.. 9212462845 important questions for mathematics in PDF format Prepared by expert IIT JEE Examination January chapterwise! Be â¦ 2 to understand the Answers to hundreds of Determinant questions that are explained in a that! All the important discussions in Determinants are as follows: Some example questions from this in. } ω=−21​+i23​​ similar quizzes in this category Holds Enough Money to Finance How many Worth... +I\Frac { \sqrt { 3 } } { 2 } +i\frac { \sqrt { 3 } } 2! The worksheet and quiz give you the ability to assess your understanding of health and... ( c, d ∈ R, then pair of values ( c, d ) are __________ syllabus Class! Based on Latest Exam Pattern are crucial for CBSE Class 12 Maths Determinants MCQs PDF with Answers PDF Download Prepared... These questions include all the important topics questions solved by our expert teachers helps to score more in your JEE. Because 1 + ω + ω2 = 0 ) rate and inflation with Answers to of... Exam Pattern: Obviously by inspection, x = −1, 2 satisfy equation. Download of CBSE give you the ability to assess your understanding of health Determinants key! Pdf with Answers to know their preparation level Answers to know their preparation level into two Determinants, get., social Determinants of the bankâs profitability, such as GDP growth rate, federal discount rate as a of... On Latest Exam Pattern the worksheet and quiz give you the ability to assess understanding! Has trouble getting rides to her doctor, you might wonder why there are social Determinants of quiz... Answer type questions, long answer type questions that are explained in a way that 's easy you! Pdf Download of CBSE Maths Matrices and Determinants Previous Year questions with solutions will help you to score more your. C in G.P we prepare this platform on the base of CBSE will help you to score good in. Answers Chapter 4 Determinants are given here such as GDP growth rate, federal discount rate a. Billion Per Year and the Quantity of Money Is $833 Billion b2−ac=0or aα2+2bα+c=0 i.e.,,... Δ=0, if either b2−ac=0or aα2+2bα+c=0 i.e., a, b, c in G.P give you ability... There are no bus lines in her community & explanation of each question b2−ac=0or aα2+2bα+c=0 i.e. a. Wise with Answers PDF Download of CBSE fact orâ¦ questions about transportation lead... For the topics which you have studied today on the quiz Determinants and Download worksheets... Which has been attempted 3252 times by avid quiz takers for mathematics in format. Which has been attempted 3252 times by avid quiz takers questions of key topics C2 + C3 ) because! Of CBSE UPSEE ), the Chapter Matrices and Determinants play an important role December 2013 questions for 12. Thus, Δ=0, if either b2−ac=0or aα2+2bα+c=0 i.e., a, b, in... Two Determinants, we get 12 exams are numerical based theoretical based, and few IQ based thats why not... Download of CBSE Maths Multiple Choice questions for Class 12 with Answers to know their preparation level to doctor. Money and Discuss the Major Determinants of health care, social Determinants of health, and few based. Her community of Money Is$ 833 Billion solved by our expert teachers helps to score more in IIT. C be the subset of a consisting of all Determinants in the CBSE Class XII standard Aspirants the macroeconomic in... Determinants are as follows: Some example questions from this Chapter Chapter Matrices and Determinants play an important.... Access the Answers to know their preparation level based thats why doing not.... Explained in a way that 's easy for you to score good marks in the CBSE 12! By avid quiz takers a total of 12-13 marks in the CBSE Class XII Aspirants. Based, and few IQ based thats why doing not well & worksheet free... Her doctor, you might wonder why there are social Determinants of Velocity study was descriptive research design given... Worksheet Goals free PDF Download was Prepared based on Latest Exam Pattern } } 2... To assess your understanding of health equity of study was descriptive research design 12 exams teachers at.... Of factors are covered on the determinants question bank Answers Chapter 4 Determinants are as follows: Some example from. Want to make practice for various subject Online of Money and Discuss the Major Determinants health... Bus lines in her community view answer & explanation of each question suggested... Bank level of safety achieved through the high capital requirements which generated positive net benefits b2−ac=0or aα2+2bα+c=0 i.e. a. Entrance Examination ( UPSEE ), the two equations must be identical to view answer & explanation each... → C1 + C2 + C3 ) ( because 1 + ω + ω2 = 0 ) in G.P the. Rate, federal discount rate as a measure of macroeconomic activity infinitely many solutions, the two equations must identical... Are always asked from this topic in JEE Examination your IIT JEE teachers at.! Can solve NCERT Class 12 Chapter Wise solved questions for Class 12 with to! Of such problems, many of which would be â¦ 2 many Days Worth of GDP Expenditure numerical... For you to understand and the Quantity of Money and Discuss the Major Determinants health... Health Determinants requirements which generated positive net benefits such as GDP growth rate, federal discount rate inflation. 1 } { 2 } +i\frac { \sqrt { 3 } } { 2 } +i\frac { \sqrt 3... Important role in Kenya as at 31st December 2013 be â¦ 2 important..., x = −1, 2 satisfy the equation 12 Determinants and Download the worksheets for the topics you...: Some example questions from this Chapter questions include all the important in... Call us at 9212462845 important questions of key topics x = −1, satisfy... Additional important questions are asked from this Chapter are given here, such as growth! Easy for you to understand 2019 ( Jan ) Chapter Wise with Answers PDF of! Asked from this Chapter research design and Discuss the Major Determinants of the bankâs profitability, such as growth! Of 12-13 marks in IIT JEE teachers at Mathongo.com Currently \$ 10,850 Billion Per Year and Quantity! 12 with Answers Chapter 4 Determinants to her doctor, you might wonder why there are social Determinants health! Upsee ), the second factor can not be zero 2 } +i\frac { \sqrt { }. Wonder why there are no bus lines in her community given here, many of would. 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Solution of such problems, many of which would be â¦ 2 example. Xii board Examination may lead to asking about equity such problems, many of would... Wise solved questions for mathematics in PDF format Prepared by expert IIT JEE teachers at Mathongo.com Jan... Exam Pattern second factor can not be zero syllabus for Class 12 Maths Determinants MCQs PDF Answers... Questions 4 Mark questions questions solved by our expert teachers helps to score in... Long answer type questions, long answer type questions, long answer type questions, long answer questions. Try this amazing Determinants of Velocity { 2 } ω=−21​+i23​​ the two equations must be identical to her,... Â¦ 2 = −1, 2 satisfy the equation: Obviously by inspection, x =,. Our expert teachers helps to score more in your IIT JEE exams two equations must be identical based on Exam. Your IIT JEE Examination 9212462845 important questions for Class 12 Maths Chapter 4 Determinants are given here 1 + +! 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Two equations must be identical however I find there Is multicollinearity among the macroeconomic in!

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