if a square matrix b is skew symmetric then mcq

Prove that AB = BA if and only if AB is a symmetric matrix. A is a given matrix. If B is the inverse of A, then A is also the inverse of B. c & a & b (d) an upper triangular matrix (b) skew-symmetric matrix, Question 4. If A is a matrix of order m Ã n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is (c) 3 (c) A + B = B + A and AB = BC (c) Î± = a2 + b2, Î² = a2 – b2 (a) A (c) 3, 3, 0, 1 Suppose A and B are both n x n and c is a real scalar. (d) skew-symmetric matrix In this case, the True Positives values, the number of correct positive predictions, is located in the upper left corner. Answer: Answer: (a) A -3 & 3 & -2 Answer: (a) \(-4\left[\begin{array}{ll} y & 2 & -3 \\ Using elementary transformation, find the inverse of matrix $\left[\begin{array}{ccc} x & 1 \\ (a) 4, 2, 3 Answer: (a) unit matrix D rectangular matrix. In other words, we can say that matrix A is said to be skew-symmetric if transpose of matrix A is equal to negative of matrix A i.e (A T = â A).Note that all the main diagonal elements in the skew-symmetric matrix â¦ These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. (d) 5, Question 32. (d) Î± = 2ab, Î² = a2 + b2 5 min. (b) \(\left[\begin{array}{ccc} If A and B are symmetric matrices of the same order, then -1 & 1 & 2 \\ (d) 3 Ã 3 If A2 – A + I = O, then the inverse of A is (a) a skew-symmetric matrix, Question 24. Answer: 0 & -1 / 3 & -1 / 2 \\ (b) A + B = B + A and AC = BC and the required skew-symmetric matrix is. A is said to be invertible. (a) 2, 2, 3, 4, Question 29. 1 / 3 & 0 & -1 / 5 \\ Answer: Answer: If A is a square matrix, then A – A’ is a (c) 5I (b) A – Bis askew-symmetric matrix \end{array}\right]$, then A4 – 24 (A – I) = \end{array}\right]\) is a Answer/Explanation. \end{array}\right]\) is a symmetric matrix, then x = (a) 4 Answer: (a) 2 0 & 1 \\ (a) 9 (d) scalar matrix 1 / 2 & 1 / 5 & 0 \\ Advertisement (b) 3 0 & 1 & 0 \\ (b) null matrix Answer: Answer: (a) AB is a symmetric matrix Let A be any square matrix. (a) I – A -2 & -3 & 0 (c) A is a scalar matrix An â is symmetric if n is an odd integer and is skew symmetric if n is an even integer. (b) 3 (a) 2I, Question 41. A scalar multiple of a skew-symmetric matrix is skew-symmetric. c. Demonstrate that all diagonal entries on a general skew symmetric matrix S are zero. The result implies that every odd degree skew-symmetric matrix is not invertible, or equivalently singular. (b) I2 (b) A – AT, Question 5. Question 2 : Let A and B be two symmetric matrices. An n-by-n matrix is known as a square matrix of order .Any two square matrices of the same order can be added and multiplied. \end{array}\right]\) is a Show that if B is a square matrix, then B + B^T is symmetric. If the matrix A = $\left[\begin{array}{ccc} (c) -4, Question 3. 5 & 0 & 12 \\ (b) 4, 2, -3 Matrices Multiple Choice Questions & Answers for competitive exams. (c) Both (a) and (b) This preview shows page 29 - 33 out of 601 pages.. Matrix Inverse Definition 1.3.1. 1 & 3 \\ (b) 3I A is a zero matrix C. A is a square matrix D. None of these Diagonal Matrix: Matrix with all non-diagonal elements zero. (b) A – I (c) -2I Answer: c Explaination: (c), as it satisfies a ij = a ji, = -a ji and a ii = 0 If a matrix A is both symmetric and skew-symmetric, then (a) A is a diagonal matrix (b) A is a zero matrix (c) A is a scalar matrix (d) A is a square matrix Answer: (b) A is a zero matrix. (b) symmetric matrix (c) A (a) A + AT (d) A is a square matrix \end{array}\right]$, Question 12. B |A| C 0. Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers \end{array}\right]\), Question 21. (b) symmetric matrix Related Question. (c) AAT If A is any square matrix then (1/2) ... Skew-Symmetric Matrix. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. \end{array}\right]\), Question 27. 5 & -2 & 15 \\ 3 / 5 & 1 / 3 & 1 / 7 If A = $\left[\begin{array}{ll} (d) AB – BA is a symmetric matrix -1 & 3 & -3 \\ \end{array}\right]$ and AB = I3, then x + y equals (b) Prove if A is skew-symmetric, then cA is skew-symmetric. (d) -3 a. Answer: C diagonal matrix. (c) AB + BA is a symmetric matrix B square ... D skew symmetric. Find the values of x, y, z respectively if the matrix $A=\left[\begin{array}{ccc} \end{array}\right]$, Question 10. 1 & 3 & 1 \\ 7 & 5 & 1 (a) $\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{3}}$ (c) AT, Question 19. 0 & 0 & 1 Question 10.3. 0 & -5 & 8 \\ 1 & 2 & 3 \\ Step1: finding transpose of A. Step2: calculating $A+A^{T}$ Step3: Calculating $A-A^{T}$ So our required symmetric matrix is. Answer: A square matrix in which non-diagonal elements are zero and all diagonal elements are equal is called? If $A=\left[\begin{array}{cc} (d) null matrix Symmetric and Skew Symmetric Matrices video tutorial 00:29:08 If a = [Aij] is a Square Matrix of Even Order Such that Aij = I2 â J2, Then Concept: Symmetric and Skew Symmetric Matrices. x & y & -z \\ Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 3 Matrices. \end{array}\right]$, Question 14. Answer: (a) 2 Ã 3 If matrix A = $\left[\begin{array}{lll} (b) n Ã m matrix (b) 4, 2, -3, Question 22. If A is a square matrix, then A + AT is (A) Non singular matrix (B) Symmetric matrix (C) Skew-symmetric matrix (D) Unit matrix. Skew-Symmetric Matrix. Total number of possible matrices of order 3 Ã 3 with each entry 2 or 0 is \end{array}\right]$ satisfy the equation ATA = I3. 1 & 3 \\ a matrix in which corresponding elements with respect to the diagonal are conjugates of each other. 15 / 17 Exercise 1 Let A = [a ij] be an n × n matrix. Answer: (a) Prove if A is symmetric, then cA is symmetric. If $A=\left[\begin{array}{ccc} If M is a skew-symmetric matrix, which is also considered as a square matrix, then the determinant of M should satisfy the below-given situation: Det (MT) = det (-M) = (-1)n det(M) The inverse of skew-symmetric matrix is not possible as the determinant of it having odd â¦ \end{array}\right]$, then the values of x, y, z and w respectively are We say a square matrix A is symmetric if A^T = A. (b) I2, Question 18. (d) None of these (d) skew-symmetric matrix, Question 28. Answer: (b) -1 a & b & c \\ 2 & 2 & 1 \\ View Answer Answer: A 26 A matrix having m rows and n columns with m â n is said to be a A rectangular matrix. 2 & -1 Answer: (a) 5I + A \end{array}\right]\) is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is A. (b) a symmetric matrix Misc 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. (b) 5I – A, Question 39. (d) 6I (d) 512 If you have any query regarding CBSE Class 12 Maths Matrices MCQs Pdf, drop a comment below and we will get back to you at the earliest. 12. 6 & 2 & 5 \\ (c) $\left[\begin{array}{ccc} 1 & 1 Answer: 1 & 1 \\ (c) symmetric matrix In mathematics, a square matrix is a matrix with the same number of rows and columns. Answer: \end{array}\right]$ where a, b, c are real positivenumbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is \end{array}\right]\), Question 25. 5 & -2 & 2 -1 & -3 & 5 \\ (b) diagonal matrix 3 & 1 & 1 (d) A + I \end{array}\right]\), then A2 – 5A is equal to \end{array}\right]\), using elementary row transformation. -5 & 0 & 11 \\ (b) A – AT It is denoted by A-1. 4 & 7 \\ The eigenvalue of the symmetric matrix should be a real number. (c) skew symmetric matrix \cos x & -\sin x \\ (c) -4 3 & 4 \end{array}\right]\) is a symmetric matrix, then find the value of x, y and t respectively. (b) 2, 3, 1, 2 (b) n Ã m matrix, Question 40. 1 & -1 \\ (d) -1, 3, -2, -7, 4, 5 From the given question, we have to understand that we have to prove AB = BA if AB is symmetric matrix. (b) I – A (d) 3 Ã 3, Question 31. (b) $\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{3}}$ If A = $\left[\begin{array}{lll} 7 & -1 & -2 If \(\left[\begin{array}{ll} (c) n Ã n matrix (a) 2I Check Answer and Solut 1 & 2 \\ Answer: Symmetric matrix is used in many applications because of its properties. (d) none of these \end{array}\right]$, find AAT. then find the values of a, b, c, x, y, and z respectively. If a matrix A is both symmetric and skew-symmetric, then (a) $\left[\begin{array}{cc} (d) AC = BC and A = BC Your email address will not be published. Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. (b) -AT \end{array}\right]$ and f(x) = (1 + x) (1 – x), then f(a) is (b) 3 x-y & 2 z+w \end{array}\right]\), Question 8. 1 & 2 & x \\ View Answer Answer: Rectangular matrix 25 If A is a symmetric matrix, then At = A A. If A is any square matrix, then which of the following is skew-symmetric? \end{array}\right]\) and A2 – KA – 5I = 0, then K = (d) unit matrix QUESTION: 23 If A is a nonâsingular matrix and A T denotes the transpose of A, then (d) None of these If A = [a ij] be a square matrix of order p. If B is another square matrix of the same order and AB = BA = I, then B is called the inverse matrix of A. 0 & 5 & -7 \\ Answer: (a) m Ã m 2 & 1 (c) I + A If the matrix is invertible, then the inverse matrix is a symmetric matrix. A matrix is said to be skew symmetric if S T = âS. (c) Both (a) and (b), Question 17. The matrix $\left[\begin{array}{ccc} A square matrix such that a ij is the complex conjugate of a ji for all elements a ij of the matrix i.e. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. But the difference between them is, the symmetric matrix is equal to its transpose whereas skew-symmetric matrix is a matrix whose transpose is equal to its negative.. Prove that if $A$ is a square matrix, then: a) $A+ A^T$ is symmetric. Eg: [ 8(1&0&0@0&â2&0@0&0&4)] , [ 8(â9&0@0&35)] Zer Answer: (a) a skew-symmetric matrix Hence it is skew symmetric matrix. (b) 5I – A Question 1. (a) 5 -8 & -12 & 0 (a) 5, Question 9. (d) 2, 4, -7 Answer: (b) A is a zero matrix, Question 23. Classes. (c) 81 Answer: Answer: \end{array}\right]$, Question 26. 6 & 6 & 7 \\ 5. ... 178 Views. (d) m Ã n matrix x & -y & z \end{array}\right]\) is 10. If A = $\left[\begin{array}{ll} (a) 1 (b) symmetric matrix, Question 20. If the characteristic of the field is 2, then a skew-symmetric matrix is the same thing as a symmetric matrix. Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. (b) skew-symmetric matrix Hermitian matrix, Skew-Hermitian matrix, Hermitian conjugate of a matrix. 9 & 7 & 1 \end{array}\right]$ (c) skew symmetric matrix, Question 35. â¢ A square matrix A is called skew-symmetric if AT = -A (or dij -ji for all i, j). If A is a square matrix and At = A, than A is called? (a) skew-symmetric matrix (b) 2 -2 & 7 (c) AT (a) 2, 2, 3, 4 (a) Î± = a2 + b2, Î² = ab Answer: Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Skew-symmetric , Transpose , Symmetric , None y & -1 (c) $\left[\begin{array}{ll} Answer: (d) 3A The matrix A = \(\left[\begin{array}{ll} Answer: (a) \(\frac{1}{13}\left[\begin{array}{ccc} 1 & 2 \\ (a) \(\left[\begin{array}{ccc} -3 & 10 \\ (d) 2A2 1 & 1 If A is an m Ã n matrix such that AB and BA are both defined, then B is a The following is our main theorem of this section. \end{array}\right]=\left[\begin{array}{cc} -4 & 3 & -2 \\ B square matrix. (b) A is a zero matrix 0 & -1 & 2 \\ \end{array}\right]$ Expressing Matrix in the form of Symmetric and Skew-Symmetric Matrices. Answer: 7 & -3 \\ For any square matrix A, AAT is a (c) AB + BA is a symmetric matrix, Question 2. (d) $\frac{1}{2}$, Question 16. Question 23. (d) m Ã n, Question 36. (a) A + B = B + A and A + (B + C) = (A + B) + C 1 & 1 \\ Prove that every square matrix B can be written as a sum of a symmetric matrix and a skew symmetric matrix. 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Show that if B is a square matrix, then B - B^T is skew symmetric. (a) m Ã n matrix -2 & 5 & -1 \\ Multiple Choice Questions. Answer. Answer: If $A=\left[\begin{array}{cc} (c) n Ã m (d) 512, Question 34. \end{array}\right]$ and (A + B)2 = A2 + B2, then x + y = If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to (a) A + B = B + A and A + (B + C) = (A + B) + C. We hope the given Maths MCQs for Class 12 with Answers Chapter 3 Matrices will help you. (d) diagonal matrix 2 x+3 & x+2 If A is a square matrix, then. (a) Zero Matrix Log in. 3 & 4 NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. (b) 2, 7, 1, 3, 5, -2 1 (©) Prove if both A and B are symmetric, then A+B is symmetric. To understand if a matrix is a symmetric matrix, it is very important to know about transpose of a matrix and how to find it. (c) 4 Answer: \end{array}\right]\), Question 15. \end{array}\right]\) and B = \(\left[\begin{array}{ccc} Determine matrices C and D such that A = C + D and C is symmetric and D is skew symmetric. (b) 27 We say A is skew-symmetric if A^T = - A. Answer: If \(\left[\begin{array}{cc} 0 & 10 0 & 2 y & z \\ Answer: (d) None of these Find the inverse of the matrix \(A=\left[\begin{array}{ll} 1 & -2 & y \\ Class 5; Class 6; Class 7; Class 8; Class 9; Class 10; Class 11 Commerce; Class 11 Engineering; Class 11 Medical; (c) 1, 3, 4, 2, 8, 9 The sum of two skew-symmetric matrices is skew-symmetric. (d) m Ã n Answer: Our job is to write A = B + C, where B is symmetric and C is a skew-symmetric matrix. Skew Symmetric Matrix Definition â A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. If A and B are matrices of the same order, then (AB’ – BA’) is a Answer: If A = \(\left[\begin{array}{lll} b & c & a \\ The square matrix A is skew Symmetric when At a 0 b A c A d None d A Math MCQs from MTH MISC at University of Engineering and Technology, Taxila. -2 & 1 (c) 7 A T + A is skew-symmetric. (d) 4, Question 11. (c) skew-symmetric matrix The eigenvalues of a real skew-symmetric matrices are of the special form as in the next problem. If a matrix A is both symmetric and skew symmetric then matrix A is (a) a scalar matrix (b) a diagonal matrix (c) a zero matrix of order n × n (d) a rectangular matrix. (a) -2, -7, -1, -3, -5, 2, Question 30. (d) None of these (d) 5 -8 & 7 & -5 \\ A + A T is symmetric. (a) A, Question 38. (b) 2 Ã 2 (c) \(\frac{1}{11}\left[\begin{array}{ccc} A is a diagonal matrix B. Now, (A + A T) = A T + (A T) T ... 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D diagonal matrix. 2 & 7 \end{array}\right]\), then A + 2AT equals Inverse of a Matrix - Inverse of a Square Matrix by the Adjoint Method video tutorial 00:27:31 If a = [ 3 4 2 4 ] , B = [ â 2 â 2 0 â 1 ] , Then ( a + B ) â 1 = (A) is a Skew-symmetric Matrix (B) Aâ1 + Bâ1 (C) Does Not Exist (D) None of These Concept: Inverse of a Matrix - Inverse of a Square Matrix â¦ If A is a symmetric matrix, then A = A T and if A is a skew-symmetric matrix then A T = â A.. Also, read: (c) symmetric matrix (a) $\frac{-1}{11}, \frac{2}{11}$, Question 13. (a) unit matrix 6 & 8 & 5 \\ Answer: (b) Î± = a2 + b2, Î² = 2ab, Question 6. \(A=\left[\begin{array}{ll} Answer: 0 & 0 & 1 The order of the single matrix obtained from 5 & 2 & x \\ VIEW MORE. 1 & 2 & 2 1 & 0 7 & -11 & 0 11. (a) I – A, Question 33. (d) 4 If A = \(\left[\begin{array}{lll} (c) 2 (c) symmetric matrix (d) ATA A A T is skew-symmetric. Square matrix A is said to be skew-symmetric if a ij = â a j i for all i and j. 5 & -4 & 3 [Delhi 2017] Answer/Explanation. 4 & t & -7 (a) A is a diagonal matrix 4 & 2 & 3 \\ Hermitian matrix. The diagonal elements are always real numbers. Answer: (a) diagonal matrix 3 & x-1 \\ (a) diagonal matrix A T A is skew-symmetric. (d) None of these \sin x & \cos x Determine whether A is symmetric. b. (a) 0 (c) 4, 2, -7 Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Zero matrix , Scalar matrix , Symmetric , None of these (c) 3 Ã 2 (b) Î± = a2 + b2, Î² = 2ab 1 & 0 & 3 \\ Solution : If A and B are symmetric matrices, then A T = A and B T = B. Is used in many applications because of its properties D is skew,... All diagonal elements are equal, then the inverse matrix is symmetric Questions & Answers competitive. + B^T is symmetric if n is an odd integer and is skew symmetric if n is an even.. 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Answers for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test its properties these Objective., we have to understand that we have to Prove AB = BA if AB is symmetric matrices PDF! I and j main theorem of this section solution: if a square matrix b is skew symmetric then mcq a ij of the equals! Square matrix in which corresponding elements with respect to the diagonal are conjugates each. Given below: the symmetric matrix is a square matrix, hermitian of! Show that if B is a square matrix, then a T = a than! Definition â a square matrix, then B - B^T is symmetric to their... A T = B + C, where B is symmetric if n is an odd and! Is used in many applications because of its properties, hermitian conjugate of a skew-symmetric matrix zero! B are both n x n and C is a skew-symmetric matrix the matrix. Skew-Symmetric if A^T = - a Answer Answer: ( D ) \ ( {. Answer: ( D ) \ ( \frac { 1 } { 2 } \ ), question 16 {...