We say A is skew-symmetric if A^T = - A. (b) skew-symmetric matrix, Question 4. (a) unit matrix The matrix \(\left[\begin{array}{ccc} (a) 2I, Question 41. (c) 5I View Answer Answer: A 26 A matrix having m rows and n columns with m ≠ n is said to be a A rectangular matrix. (b) A – Bis askew-symmetric matrix (d) None of these -8 & 7 & -5 \\ 1 & 1 \\ Answer: (c) skew-symmetric matrix (a) A, Question 38. Answer: \end{array}\right]\), then A2 – 5A is equal to (b) I – A (c) skew symmetric matrix -2 & 5 & -1 \\ (b) -1 If A is a square matrix, then. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. 1 & 2 & 2 Question 23. Determine whether A is symmetric. 1 & 2 \\ \end{array}\right]\) and (A + B)2 = A2 + B2, then x + y = If the matrix A = \(\left[\begin{array}{ccc} If M is a skew-symmetric matrix, which is also considered as a square matrix, then the determinant of M should satisfy the below-given situation: Det (MT) = det (-M) = (-1)n det(M) The inverse of skew-symmetric matrix is not possible as the determinant of it having odd … B |A| C 0. -5 & 0 & 11 \\ \end{array}\right]\) and AB = I3, then x + y equals (b) A is a zero matrix If A is a symmetric matrix, then A = A T and if A is a skew-symmetric matrix then A T = – A.. Also, read: (d) -3 Now, (A + A T) = A T + (A T) T ... B are two square matrices such that AB = A and BA = B, then prove that B 2 = B. 1 / 2 & 1 / 5 & 0 \\ (b) 4, 2, -3 Answer: Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Zero matrix , Scalar matrix , Symmetric , None of these (d) none of these (b) \(\left[\begin{array}{cc} If A = \(\left[\begin{array}{ll} Answer: (a) 9 4 & 2 & 3 \\ 7 & -1 & -2 Step 3-If the transpose matrix and the original matrix are equal , then the matrix is symmetric. (c) AB + BA is a symmetric matrix 0 & 2 y & z \\ It is denoted by A-1. Answer: \end{array}\right]\), then A4 – 24 (A – I) = Hermitian matrix. The eigenvalue of the symmetric matrix should be a real number. (b) 3 (d) None of these >वर्तमान में ‘सम्पत्ति का अधिकार’ किस प्रकार का अधिकार है ? Find the values of x, y, z respectively if the matrix \(A=\left[\begin{array}{ccc} If A is a square matrix, then A + AT is (A) Non singular matrix (B) Symmetric matrix (C) Skew-symmetric matrix (D) Unit matrix. (a) I – A, Question 33. (c) 2 5 & -4 & 3 (b) a symmetric matrix Find the inverse of the matrix \(A=\left[\begin{array}{ll} Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. (a) \(-4\left[\begin{array}{ll} A scalar multiple of a skew-symmetric matrix is skew-symmetric. (b) A is a zero matrix, Question 23. (d) m × n matrix x+y & 2 x+z \\ 1 & -2 & y \\ -4 & 3 & -2 \\ Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers Answer: (b) 3I 1 & 1 The matrix \(\left[\begin{array}{ccc} Answer: Answer: If A = [a ij] be a square matrix of order p. If B is another square matrix of the same order and AB = BA = I, then B is called the inverse matrix of A. Prove that AB = BA if and only if AB is a symmetric matrix. 0 & -1 & 1 \\ 0 & -1 / 3 & -1 / 2 \\ (b) diagonal matrix 5 & 2 & x \\ (b) 5I – A \end{array}\right]\) is 1 & 2 & 3 \\ For any square matrix A, AAT is a Answer: Answer: (a) 2I (c) \(\left[\begin{array}{ll} If \(A=\left[\begin{array}{ccc} (b) 3 Answer: -1 & 3 & -3 \\ VIEW MORE. 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. 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 = − A).Note that all the main diagonal elements in the skew-symmetric matrix … 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. Symmetric matrix is used in many applications because of its properties. [Delhi 2017] Answer/Explanation. (d) 3 × 3 Answer: -1 & 1 & 2 \\ (b) \(\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{3}}\) (d) 6I NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. (c) 1, 3, 4, 2, 8, 9 1 & 2 & x \\ 1 & 1 \\ y & 2 & -3 \\ (c) α = a2 + b2, β = a2 – b2 3 & 4 An → is symmetric if n is an odd integer and is skew symmetric if n is an even integer. \end{array}\right]\) is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is (a) A A A T is skew-symmetric. Answer: 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. (a) A + AT Answer. 1 & 1 4 & 7 \\ (c) skew symmetric matrix, Question 35. \end{array}\right]\) is a x & 1 \\ \end{array}\right]=\left[\begin{array}{cc} (a) 2 (a) \(\frac{1}{13}\left[\begin{array}{ccc} A matrix is said to be skew symmetric if S T = −S. If A is a square matrix and At = A, than A is called? 0 & 5 & -7 \\ 10. 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