If \(A=\left[\begin{array}{cc} (d) 3 × 3, Question 31. \end{array}\right]\) is a 7 & -1 & -2 \end{array}\right]\), then the values of x, y, z and w respectively are \end{array}\right]\), find AAT. -8 & -12 & 0 (b) A + B = B + A and AC = BC These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. (b) A – I (c) 1, 3, 4, 2, 8, 9 (b) a symmetric matrix Question 23. 1 & 2 & 3 \\ Answer: 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.. Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. \end{array}\right]\), Question 27. If A = \(\left[\begin{array}{lll} 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. If A is any square matrix, then which of the following is skew-symmetric? 1 & 1 A square matrix such that a ij is the complex conjugate of a ji for all elements a ij of the matrix i.e. (a) -2, -7, -1, -3, -5, 2, Question 30. Answer: (a) 2 1 & 2 \\ If \(A=\left[\begin{array}{ccc} D diagonal matrix. \end{array}\right]\) is a symmetric matrix, then find the value of x, y and t respectively. x & y & -z \\ Answer: Answer: [Delhi 2017] Answer/Explanation. Using elementary transformation, find the inverse of matrix \(\left[\begin{array}{ccc} \end{array}\right], B=\left[\begin{array}{ll} -5 & 0 & 11 \\ 7 & 5 & 1 (c) n × m \end{array}\right]\) and AB = I3, then x + y equals The order of the single matrix obtained from Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Skew-symmetric , Transpose , Symmetric , None (a) unit matrix (c) symmetric matrix (c) -4, Question 3. (d) 4, Question 11. (d) ATA 1 & 2 \\ Answer: \cos x & -\sin x \\ (c) symmetric matrix 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. If the matrix is invertible, then the inverse matrix is a symmetric matrix. 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(c) Both (a) and (b), Question 17. (b) 3 A square matrix in which non-diagonal elements are zero and all diagonal elements are equal is called? Answer: (a) AB is a symmetric matrix If A is a square matrix, then. (c) A + B = B + A and AB = BC \end{array}\right]\) and A2 – KA – 5I = 0, then K = Answer: c Explaination: (c), as it satisfies a ij = a ji, = -a ji and a ii = 0 Answer: Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers x+y & 2 x+z \\ (a) a skew-symmetric matrix (c) α = a2 + b2, β = a2 – b2 \end{array}\right]\), using elementary row transformation. If a matrix A is both symmetric and skew-symmetric, then (d) α = 2ab, β = a2 + b2 0 & 0 & 1 The eigenvalues of a real skew-symmetric matrices are of the special form as in the next problem. (d) 2, 4, -7 0 & 10 12. Answer: From the given question, we have to understand that we have to prove AB = BA if AB is symmetric matrix. ... 178 Views. \end{array}\right]\) is Answer: (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. 3 / 5 & 1 / 3 & 1 / 7 (d) an upper triangular matrix (d) None of these (c) AT, Question 19. A + A T is symmetric. (a) I – A (a) \(-4\left[\begin{array}{ll} If A is a square matrix and At = A, than A is called? Now, (A + A T) = A T + (A T) T ... B are two square matrices such that AB = A and BA = B, then prove that B 2 = B. 1 (©) Prove if both A and B are symmetric, then A+B is symmetric. Hermitian matrix, Skew-Hermitian matrix, Hermitian conjugate of a matrix. (d) -3 \end{array}\right]\) is a symmetric matrix, then x = (c) 81 (c) AAT Hermitian matrix. Answer: (c) 2 (a) 5, Question 9. (d) m × n, Question 36. If \(A=\left[\begin{array}{cc} (a) A (c) skew symmetric matrix A symmetric matrix and skew-symmetric matrix both are square matrices. Answer: 1 & -1 \\ 0 & -1 & 2 \\ \end{array}\right]\), Question 15. x & -y & z \end{array}\right]\) and (A + B)2 = A2 + B2, then x + y = y & -1 Answer: (d) skew-symmetric matrix, Question 28. (a) 2 × 3 (a) \(\left[\begin{array}{ccc} (a) Zero Matrix Answer: If A = \(\left[\begin{array}{lll} (b) 4, 2, -3, Question 22. 0 & 0 & 1 2 & 1 (c) -2I c & a & b 1 & 1 \\ (b) 3 (b) α = a2 + b2, β = 2ab If \(\left[\begin{array}{cc} Answer: \end{array}\right]\) where a, b, c are real positivenumbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is and the required skew-symmetric matrix is. Hence it is skew symmetric matrix. 6 & 6 & 7 \\ 6 & 2 & 5 \\ (b) n × n y & 2 & -3 \\ Prove that if $A$ is a square matrix, then: a) $A+ A^T$ is symmetric. Misc 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. Answer: (d) 4 The matrix \(\left[\begin{array}{ccc} (b) I – A \end{array}\right]\), Question 12. Answer: Answer: (c) -4 Question 10.3. 3 & 1 & 1 (b) skew-symmetric matrix, Question 4. (b) symmetric matrix, Question 20. (d) 3A (a) \(\frac{-1}{11}, \frac{2}{11}\), Question 13. (a) A, Question 38. Answer: (a) 2, 2, 3, 4, Question 29. (d) -1, 3, -2, -7, 4, 5 (d) diagonal 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 … 1 & 3 \\ The diagonal elements are always real numbers. Skew Symmetric Matrix Definition – A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. This preview shows page 29 - 33 out of 601 pages.. Matrix Inverse Definition 1.3.1. (c) symmetric matrix C diagonal matrix. (d) None of these 1 / 3 & 0 & -1 / 5 \\ A T + A is skew-symmetric. 1 & -2 & y \\ (b) I2, Question 18. \end{array}\right]\), Question 25. (c) \(\frac{1}{11}\left[\begin{array}{ccc} 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. Answer: (c) Both (a) and (b) Step 3-If the transpose matrix and the original matrix are equal , then the matrix is symmetric. (a) 5 (a) A + AT Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Zero matrix , Scalar matrix , Symmetric , None of these If A and B are symmetric matrices of the same order, then (a) m × m If A is an m × n matrix such that AB and BA are both defined, then B is a (b) A – AT, Question 5. (b) 27 (d) 512 5. 2 & 7 (a) 9 (d) unit matrix 9 & 7 & 1 b) $A-A^T$ is skew-symmetric. If B is the inverse of A, then A is also the inverse of B. (b) 2 x-y & 2 z+w 0 & 2 y & z \\ Answer: (a) 1 Related Question. Answer: (d) 3 × 3 Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. (a) m × n matrix In mathematics, a square matrix is a matrix with the same number of rows and columns. (b) 2 × 2 1 & 2 & x \\ Show that if B is a square matrix, then B - B^T is skew symmetric. 3 & 4 (b) 5I – A, Question 39. Prove that AB = BA if and only if AB is a symmetric matrix. Answer: 7 & -11 & 0 Symmetric and Skew Symmetric Matrices video tutorial 00:29:08 If a = [Aij] is a Square Matrix of Even Order Such that Aij = I2 − J2, Then Concept: Symmetric and Skew Symmetric Matrices. -8 & 7 & -5 \\ (b) 4, 2, -3 A. If A = \(\left[\begin{array}{lll} A matrix is said to be skew symmetric if S T = −S. \end{array}\right]\), then A + 2AT equals Determine whether A is symmetric. 1 & 0 -1 & 1 & 2 \\ If A = \(\left[\begin{array}{ll} (b) A is a zero matrix, Question 23. \end{array}\right]\), Question 10. -2 & 7 (a) 2I 0 & -1 / 3 & -1 / 2 \\ Eg: [ 8(1&0&0@0&−2&0@0&0&4)] , [ 8(−9&0@0&35)] Zer (b) A – AT (b) symmetric matrix 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. View Answer Answer: A 26 A matrix having m rows and n columns with m ≠ n is said to be a A rectangular matrix. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. And columns can solve NCERT Class 12 with Answers Chapter 3 matrices Objective Questions with Answers Chapter 3.. 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