The eigenvalue of the symmetric matrix should be a real number. â¢ A square matrix A is called skew-symmetric if AT = -A (or dij -ji for all i, j). (b) skew-symmetric matrix The result implies that every odd degree skew-symmetric matrix is not invertible, or equivalently singular. (d) 3 Ã 3, Question 31. \end{array}\right]\), Question 25. (c) A + B = B + A and AB = BC A square matrix in which non-diagonal elements are zero and all diagonal elements are equal is called? 7 & -3 \\ (c) skew-symmetric matrix b) $A-A^T$ is skew-symmetric. Log in. 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.. (a) 1 The matrix A = \(\left[\begin{array}{ll} If \(A=\left[\begin{array}{cc} (c) a diagonal matrix (d) m Ã n \end{array}\right]=\left[\begin{array}{cc} \end{array}\right]\), then A + 2AT equals (d) none of these a matrix in which corresponding elements with respect to the diagonal are conjugates of each other. 1 & -1 & 1 \\ 4 & 7 \\ (c) n Ã m 2 & 7 (a) 5, Question 9. \end{array}\right]\), Question 15. x & y & -z \\ Answer: Class 5; Class 6; Class 7; Class 8; Class 9; Class 10; Class 11 Commerce; Class 11 Engineering; Class 11 Medical; If A and B are matrices of the same order, then (AB’ – BA’) is a The matrix \(\left[\begin{array}{ccc} The matrix \(\left[\begin{array}{ccc} Check Answer and Solut (c) symmetric matrix \end{array}\right]\), Question 12. (d) 512, Question 34. 1 & -1 \\ We say A is skew-symmetric if A^T = - A. (c) AB + BA is a symmetric matrix, Question 2. (d) diagonal matrix Answer: If a matrix A is both symmetric and skew-symmetric, then 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. Related Question. 0 & 1 \\ Answer: 1 & 2 & x \\ (b) 2 \end{array}\right]\), then the values of x, y, z and w respectively are Matrices Multiple Choice Questions & Answers for competitive exams. An â is symmetric if n is an odd integer and is skew symmetric if n is an even integer. (a) diagonal matrix (a) 5I + A Answer: View Answer Answer: Rectangular matrix 25 If A is a symmetric matrix, then At = A A. Advertisement (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. In this case, the True Positives values, the number of correct positive predictions, is located in the upper left corner. Answer: Using elementary transformation, find the inverse of matrix \(\left[\begin{array}{ccc} \end{array}\right]\) is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is y & 2 & -3 \\ 0 & 0 & 1 (a) 4 Answer: Prove that AB = BA if and only if AB is a symmetric matrix. Find the values of x, y, z respectively if the matrix \(A=\left[\begin{array}{ccc} (a) m Ã m 3 & 1 & 1 (a) A (d) AC = BC and A = BC B square matrix. We say a square matrix A is symmetric if A^T = A. (b) A – I 3 / 5 & 1 / 3 & 1 / 7 1 & 3 \\ (a) 2, 2, 3, 4 1 & 1 3 & 4 If A = \(\left[\begin{array}{lll} Answer: Solution : If A and B are symmetric matrices, then A T = A and B T = B. A + A T is symmetric. 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. 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