(d) ATA Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. (a) 2 Ã 3 2 x+3 & x+2 and the required skew-symmetric matrix is. Total number of possible matrices of order 3 Ã 3 with each entry 2 or 0 is 3 & 4 (b) I2 A is said to be invertible. b) $A-A^T$ is skew-symmetric. (b) 3 (a) \(A=\left[\begin{array}{lll} \end{array}\right]\) and B = \(\left[\begin{array}{ccc} Solution : If A and B are symmetric matrices, then A T = A and B T = B. Symmetric and Skew Symmetric Matrices video tutorial 00:29:08 If a = [Aij] is a Square Matrix of Even Order Such that Aij = I2 â J2, Then Concept: Symmetric and Skew Symmetric Matrices. D rectangular matrix. (c) AB + BA is a symmetric matrix (b) Prove if A is skew-symmetric, then cA is skew-symmetric. (b) symmetric matrix, Question 20. (c) Both (a) and (b) (d) Î± = 2ab, Î² = a2 + b2 (a) Prove if A is symmetric, then cA is symmetric. Answer: A T + A is skew-symmetric. Expressing Matrix in the form of Symmetric and Skew-Symmetric Matrices. If the matrix is invertible, then the inverse matrix is a symmetric matrix. (d) -3 \end{array}\right]\), Question 14. (a) 5I + A 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. 1 & 2 & x \\ -2 & -3 & 0 (b) 4, 2, -3, Question 22. 1 & -1 & 1 \\ Log in. -2 & 5 & -1 \\ (d) 4, Question 11. 1 & 3 & 1 \\ QUESTION: 23 If A is a nonâsingular matrix and A T denotes the transpose of A, then (b) I2, Question 18. Answer: 1 & 0 (d) None of these (b) 2, 3, 1, 2 (b) -AT Answer: 0 & 0 & 1 These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. (a) \(\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{3}}\) If A is any square matrix then (1/2) ... Skew-Symmetric Matrix. If \(A=\left[\begin{array}{cc} If \(A=\left[\begin{array}{cc} (d) scalar matrix (d) None of these 1 & 3 \\ A symmetric matrix and skew-symmetric matrix both are square matrices. 5 & -4 & 3 Answer: ... 178 Views. Answer: \(A=\left[\begin{array}{ll} If A is a square matrix, then A – A’ is a 2 & 1 (a) \(\frac{-1}{11}, \frac{2}{11}\), Question 13. a. (d) AB – BA is a symmetric matrix 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. 1 / 2 & 1 / 5 & 0 \\ Answer: Question 1. (a) \(\frac{1}{13}\left[\begin{array}{ccc} (c) 4 -2 & 1 Advertisement (a) I – A If \(\left[\begin{array}{cc} 3 & 1 & 1 (a) 0, Question 7. \end{array}\right]=\left[\begin{array}{cc} Find the inverse of the matrix \(A=\left[\begin{array}{ll} (c) \(\left[\begin{array}{ll} We say a square matrix A is symmetric if A^T = A. Skew Symmetric Matrix Definition â A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. (a) m Ã n matrix \end{array}\right]\), Question 26. Multiple Choice Questions. Related Question. Our job is to write A = B + C, where B is symmetric and C is a skew-symmetric matrix. 1 & 2 & 3 \\ If A is an m Ã n matrix such that AB and BA are both defined, then B is a Answer: 1 / 3 & 0 & -1 / 5 \\ Answer: If A and B are matrices of the same order, then (AB’ – BA’) is a Answer: (a) diagonal matrix 0 & -1 & 2 \\ x & 1 \\ \end{array}\right]\), then the values of x, y, z and w respectively are A is a diagonal matrix B. 5 & 2 & x \\ If A = \(\left[\begin{array}{ll} \end{array}\right]\), using elementary row transformation. (b) symmetric matrix The following is our main theorem of this section. 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