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 … Skew-Symmetric Matrix. (d) skew-symmetric matrix If A is a square matrix and At = A, than A is called? Answer: -1 & 1 & 2 \\ A T + A is skew-symmetric. Answer: (a) skew-symmetric matrix (d) AB – BA is a symmetric matrix If matrix A = \(\left[\begin{array}{lll} -1 & 3 & -3 \\ Answer: 3 / 5 & 1 / 3 & 1 / 7 Step1: finding transpose of A. Step2: calculating \(A+A^{T}\) Step3: Calculating \(A-A^{T}\) So our required symmetric matrix is. Using elementary transformation, find the inverse of matrix \(\left[\begin{array}{ccc} B square matrix. If the matrix A = \(\left[\begin{array}{ccc} (a) 2 × 3 0 & -1 & 2 \\ \end{array}\right]\) is a symmetric matrix, then find the value of x, y and t respectively. 7 & -11 & 0 A is a diagonal matrix B. (c) 1, 3, 4, 2, 8, 9 11. Answer: If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to \sin x & \cos x 0 & 1 & 0 \\ Prove that if $A$ is a square matrix, then: a) $A+ A^T$ is symmetric. (a) Zero Matrix Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is (a) -2, -7, -1, -3, -5, 2 Class 5; Class 6; Class 7; Class 8; Class 9; Class 10; Class 11 Commerce; Class 11 Engineering; Class 11 Medical; 2 & 7 (a) \(\frac{1}{13}\left[\begin{array}{ccc} We say a square matrix A is symmetric if A^T = A. (c) \(\frac{1}{11}\left[\begin{array}{ccc} Answer: (d) m × n matrix \end{array}\right]\) and A2 – KA – 5I = 0, then K = (b) I – A If A = \(\left[\begin{array}{lll} Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. Answer: 1 & 1 (d) 4, Question 11. 12. 1 & 1 \\ (c) n × n matrix (d) 512, Question 34. Find the inverse of the matrix \(A=\left[\begin{array}{ll} (d) None of these 2 & -1 (b) 2 × 2 -3 & 10 \\ 1 & 3 \\ (b) A is a zero matrix, Question 23. (a) \(\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{3}}\) \end{array}\right]\), Question 15. (b) skew-symmetric matrix, Question 4. Question 10.3. 0 & 10 c. Demonstrate that all diagonal entries on a general skew symmetric matrix S are zero. (c) skew-symmetric matrix (d) m × n 0 & 2 y & z \\ (a) a skew-symmetric matrix Answer: x-y & 2 z+w (d) 5 \end{array}\right]\), find AAT. (c) 3 × 2 (d) an upper triangular matrix An → is symmetric if n is an odd integer and is skew symmetric if n is an even integer. (d) skew-symmetric matrix, Question 28. Solution : If A and B are symmetric matrices, then A T = A and B T = B. \end{array}\right]\), then A4 – 24 (A – I) = (b) A – I (b) -AT \end{array}\right]\), Question 10. 3 & 1 & 1 b & c & a \\ (d) none of these (d) -3 Answer: Eg: [ 8(1&0&0@0&−2&0@0&0&4)] , [ 8(−9&0@0&35)] Zer Show that if B is a square matrix, then B - B^T is skew symmetric. (c) n × m Question 23. (d) None of these Answer: D diagonal matrix. 1 & 3 & 1 \\ (b) \(\left[\begin{array}{cc} (a) 2, 2, 3, 4, Question 29. (a) m × m 7 & -3 \\ Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Skew-symmetric , Transpose , Symmetric , None (c) A + B = B + A and AB = BC (b) n × n Show that A − A T is skew symmetric. Answer: If A2 – A + I = O, then the inverse of A is b) $A-A^T$ is skew-symmetric. (b) α = a2 + b2, β = 2ab NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. (a) unit matrix Log in. (c) 4, 2, -7 (d) A + I 1 & 1 \end{array}\right]\), Question 14. (d) scalar matrix 6 & 8 & 5 \\ Answer: We say A is skew-symmetric if A^T = - A. (c) AAT B square ... D skew symmetric. A square matrix such that a ij is the complex conjugate of a ji for all elements a ij of the matrix i.e. 7 & 5 & 1 (c) symmetric matrix x & 1 \\ 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. x & -y & z -8 & -12 & 0 (d) 2A2 (d) α = 2ab, β = a2 + b2 If A and B are matrices of the same order, then (AB’ – BA’) is a (a) A (b) 4, 2, -3 Hence it is skew symmetric matrix. If A is any square matrix then (1/2) ... Skew-Symmetric Matrix. Skew Symmetric Matrix Definition – A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. (b) \(\left[\begin{array}{ccc} If A = \(\left[\begin{array}{ll} Question 2 : Let A and B be two symmetric matrices. (a) \(\frac{-1}{11}, \frac{2}{11}\), Question 13. (a) 1 A is a zero matrix C. A is a square matrix D. None of these Diagonal Matrix: Matrix with all non-diagonal elements zero. -5 & 0 & 11 \\ (b) α = a2 + b2, β = 2ab, Question 6. 5 min. 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. (c) A 0 & 5 & -7 \\ y & -1 \end{array}\right]\) is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is (c) \(\left[\begin{array}{ccc} A square matrix in which non-diagonal elements are zero and all diagonal elements are equal is called? (b) 2, 3, 1, 2 (d) None of these The diagonal elements are always real numbers. Answer: \cos x & -\sin x \\ 3 & 4 \end{array}\right]\) -1 & -3 & 5 \\ x & y & -z \\ -2 & 1 From the given question, we have to understand that we have to prove AB = BA if AB is symmetric matrix. (b) \(\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{3}}\) (c) a diagonal matrix RD Sharma Class 11 Solutions Free PDF Download, NCERT Solutions for Class 12 Computer Science (Python), NCERT Solutions for Class 12 Computer Science (C++), NCERT Solutions for Class 12 Business Studies, NCERT Solutions for Class 12 Micro Economics, NCERT Solutions for Class 12 Macro Economics, NCERT Solutions for Class 12 Entrepreneurship, NCERT Solutions for Class 12 Political Science, NCERT Solutions for Class 11 Computer Science (Python), NCERT Solutions for Class 11 Business Studies, NCERT Solutions for Class 11 Entrepreneurship, NCERT Solutions for Class 11 Political Science, NCERT Solutions for Class 11 Indian Economic Development, NCERT Solutions for Class 10 Social Science, NCERT Solutions For Class 10 Hindi Sanchayan, NCERT Solutions For Class 10 Hindi Sparsh, NCERT Solutions For Class 10 Hindi Kshitiz, NCERT Solutions For Class 10 Hindi Kritika, NCERT Solutions for Class 10 Foundation of Information Technology, NCERT Solutions for Class 9 Social Science, NCERT Solutions for Class 9 Foundation of IT, PS Verma and VK Agarwal Biology Class 9 Solutions, MCQs for Class 12 Chapter Wise with Answers, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, Periodic Classification of Elements Class 10, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, CBSE Previous Year Question Papers Class 12, CBSE Previous Year Question Papers Class 10. 1 & 2 & x \\ 1 & 2 \\ y & 2 & -3 \\ Answer: c Explaination: (c), as it satisfies a ij = a ji, = -a ji and a ii = 0 Determine whether A is symmetric. 1 & 1 \\ 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) \(A=\left[\begin{array}{lll} (b) 27 \end{array}\right]\) is Answer/Explanation. (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. The following is our main theorem of this section. then find the values of a, b, c, x, y, and z respectively. \end{array}\right]\), Question 21. Let A be any square matrix. A symmetric matrix and skew-symmetric matrix both are square matrices. The matrix \(\left[\begin{array}{ccc} A scalar multiple of a skew-symmetric matrix is skew-symmetric. Answer: (b) A – AT, Question 5. (d) \(\frac{1}{2}\), Question 16. Answer: Answer: (a) diagonal 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 − J2, Then Concept: Symmetric and Skew Symmetric Matrices. (d) diagonal matrix (a) A + B = B + A and A + (B + C) = (A + B) + C 1 & 0 & 3 \\ (a) 4, 2, 3 Step 3-If the transpose matrix and the original matrix are equal , then the matrix is symmetric. 1 & 0 (c) AB + BA is a symmetric matrix, Question 2. Determine matrices C and D such that A = C + D and C is symmetric and D is skew symmetric. 1 & -1 \\ 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. (a) A Classes. x+y & 2 x+z \\ [Delhi 2017] Answer/Explanation. 1 & 2 \\ (a) Prove if A is symmetric, then cA is symmetric. (c) skew symmetric matrix, Question 35. A is a given matrix. (a) 9 6 min. A + A T is symmetric. \end{array}\right]\) and AB = I3, then x + y equals Hermitian matrix. 15 / 17 Exercise 1 Let A = [a ij] be an n × n matrix. -2 & 5 & -1 \\ 0 & 1 & 0 \\ Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Zero matrix , Scalar matrix , Symmetric , None of these Answer: (c) 4 \end{array}\right]\), Question 26. (b) A + B = B + A and AC = BC (b) skew-symmetric matrix ... 178 Views. (c) Both (a) and (b), Question 17. If \(\left[\begin{array}{cc} In this case, the True Positives values, the number of correct positive predictions, is located in the upper left corner. If A is a symmetric matrix, then A = A T and if A is a skew-symmetric matrix then A T = – A.. Also, read: (a) 5 Answer: (c) Both (a) and (b) Answer: 1 (©) Prove if both A and B are symmetric, then A+B is symmetric. b. (a) A is a diagonal matrix If the characteristic of the field is 2, then a skew-symmetric matrix is the same thing as a symmetric matrix. View Answer Answer: Rectangular matrix 25 If A is a symmetric matrix, then At = A A. Answer: If A is an m × n matrix such that AB and BA are both defined, then B is a (d) A is a square matrix A A T is skew-symmetric. (b) symmetric matrix, Question 20. \end{array}\right]\), using elementary row transformation. Advertisement (b) symmetric matrix Answer: B |A| C 0. If \(A=\left[\begin{array}{cc} a. A is said to be invertible. (a) 5I + A Answer: D rectangular matrix. (d) 4 0 & 0 & 1 The matrix A = \(\left[\begin{array}{ll} 1 a ij = i 2 + j 2 2 a ij = i 2-j 2 2 A square matrix is said to be skew-symmetric if A T = - A. Answer: (b) 5I – A, Question 39. Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. 2 x+3 & x+2 \end{array}\right]\), Question 27. Answer: The sum of two skew-symmetric matrices is skew-symmetric. -8 & 7 & -5 \\ In mathematics, a square matrix is a matrix with the same number of rows and columns. (c) 2 3 & x-1 \\ C diagonal matrix. Multiple Choice Questions. (b) n × m matrix If A and B are symmetric matrices of the same order, then Answer: This preview shows page 29 - 33 out of 601 pages.. Matrix Inverse Definition 1.3.1. If A is a square matrix, then A – A’ is a (c) skew symmetric matrix Answer: 4 & 2 & 3 \\ (d) 512 (a) A + AT 0 & -1 / 3 & -1 / 2 \\ Symmetric matrix is used in many applications because of its properties. (d) 6I • A square matrix A is called skew-symmetric if AT = -A (or dij -ji for all i, j). 10. Answer: (d) null matrix (c) 5I (a) A, Question 38. \end{array}\right]\) and f(x) = (1 + x) (1 – x), then f(a) is Answer: A matrix is said to be skew symmetric if S T = −S. If A is a matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is (d) m × n, Question 36. -3 & 3 & -2 Answer: Answer: 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 … 5 & -2 & 15 \\ The result implies that every odd degree skew-symmetric matrix is not invertible, or equivalently singular. (a) \(\left[\begin{array}{ccc} 0 & -1 & 1 \\ Answer: Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. \end{array}\right]\) satisfy the equation ATA = I3. (d) 3 × 3 (b) n × m matrix, Question 40. (a) diagonal matrix (b) I2 \end{array}\right]\) (c) AB + BA is a symmetric matrix (b) Prove if A is skew-symmetric, then cA is skew-symmetric. (d) None of these (c) 81 (a) m × n matrix \end{array}\right]\) and B = \(\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. Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers (c) 3 \end{array}\right]=\left[\begin{array}{cc} (b) I2, Question 18. If A = \(\left[\begin{array}{lll} Answer: \end{array}\right]\), then A2 – 5A is equal to 0 & 0 & 1 It is denoted by A-1. (b) diagonal matrix 1 & -1 & 1 \\ 1 & 2 & 2 (c) A is a scalar matrix (c) 3, 3, 0, 1 The eigenvalue of the symmetric matrix should be a real number. (c) I + A Your email address will not be published. (a) a skew-symmetric matrix, Question 24. If a matrix A is both symmetric and skew-symmetric, then \end{array}\right], B=\left[\begin{array}{ll} Show that if B is a square matrix, then B + B^T is symmetric. (c) 7 Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 3 Matrices. 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. 2 & 2 & 1 \\ (a) I – A, Question 33. A. Answer: (a) 2I, Question 41. (a) \(\left[\begin{array}{cc} An n-by-n matrix is known as a square matrix of order .Any two square matrices of the same order can be added and multiplied. \end{array}\right]\) is a \end{array}\right]\) where a, b, c are real positivenumbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is A T A is skew-symmetric. VIEW MORE. 6 & 6 & 7 \\ Answer: View Answer Answer: A 26 A matrix having m rows and n columns with m ≠ n is said to be a A rectangular matrix. Answer: Hermitian matrix, Skew-Hermitian matrix, Hermitian conjugate of a matrix. Answer. \end{array}\right]\), then the values of x, y, z and w respectively are The eigenvalues of a real skew-symmetric matrices are of the special form as in the next problem. 2 & 1 (b) 3 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. 5 & -2 & 2 (b) 5I – A Misc 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. 1 / 3 & 0 & -1 / 5 \\ If A is any square matrix, then which of the following is skew-symmetric? (c) symmetric matrix Answer: (b) 2, 7, 1, 3, 5, -2 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.. (b) A – AT (a) AB is a symmetric matrix Answer: Answer: \end{array}\right]\) and (A + B)2 = A2 + B2, then x + y = (b) a symmetric matrix -2 & -3 & 0 1 & 2 & 3 \\ a matrix in which corresponding elements with respect to the diagonal are conjugates of each other. (a) -2, -7, -1, -3, -5, 2, Question 30. (b) A – Bis askew-symmetric matrix Check Answer and Solut Expressing Matrix in the form of Symmetric and Skew-Symmetric Matrices. (d) unit matrix (c) -4 QUESTION: 23 If A is a non–singular matrix and A T denotes the transpose of A, then The matrix \(\left[\begin{array}{ccc} (c) -4, Question 3. 1 / 2 & 1 / 5 & 0 \\ (d) None of these A + A T is symmetric. a & b & c \\ (b) 3 If \(A=\left[\begin{array}{cc} If the matrix is invertible, then the inverse matrix is a symmetric matrix. If A = \(\left[\begin{array}{lll} Prove that AB = BA if and only if AB is a symmetric matrix. (d) 3 × 3, Question 31. Question 1. Our job is to write A = B + C, where B is symmetric and C is a skew-symmetric matrix. (a) I – A (b) 2 \(A=\left[\begin{array}{ll} c & a & b Answer: 0 & 1 \\ 6 & 2 & 5 \\ 3 & 4 (a) skew-symmetric matrix, Question 37. Answer: Also, this means that each odd degree skew-symmetric matrix has the eigenvalue $0$. 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(b) symmetric matrix 5 & 2 & x \\ (a) 2I Inverse of a Matrix - Inverse of a Square Matrix by the Adjoint Method video tutorial 00:27:31 If a = [ 3 4 2 4 ] , B = [ − 2 − 2 0 − 1 ] , Then ( a + B ) − 1 = (A) is a Skew-symmetric Matrix (B) A−1 + B−1 (C) Does Not Exist (D) None of These Concept: Inverse of a Matrix - Inverse of a Square Matrix … These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. (a) 5, Question 9. \end{array}\right]\), Question 25. (a) 4 (d) AC = BC and A = BC (c) AT, Question 19. \end{array}\right]\) is a symmetric matrix, then x = Suppose A and B are both n x n and c is a real scalar. (a) α = a2 + b2, β = ab (c) -2I (a) 2, 2, 3, 4 (a) 0, Question 7. (d) 3A If \(\left[\begin{array}{ll} (b) null matrix >वर्तमान में ‘सम्पत्ति का अधिकार’ किस प्रकार का अधिकार है ? -2 & 7 (a) unit matrix and the required skew-symmetric matrix is. If \(A=\left[\begin{array}{ccc} (c) \(\left[\begin{array}{ll} \end{array}\right]\), then A + 2AT equals Prove that every square matrix B can be written as a sum of a symmetric matrix and a skew symmetric matrix. (d) -1, 3, -2, -7, 4, 5 Matrices Multiple Choice Questions & Answers for competitive exams. \end{array}\right]\) is a (d) ATA (b) -1 -4 & 3 & -2 \\ (b) A is a zero matrix 5 & -4 & 3 (b) 3I The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. 4 & t & -7 5 & 0 & 12 \\ 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. 4 & 7 \\ The order of the single matrix obtained from (c) symmetric matrix (a) 0 Related Question. If A is a square matrix, then. (a) 2 If A = \(\left[\begin{array}{ll} (c) AT 1 & -2 & y \\ If B is the inverse of A, then A is also the inverse of B. 0 & -5 & 8 \\ (c) α = a2 + b2, β = a2 – b2 (a) \(-4\left[\begin{array}{ll} \end{array}\right]\), Question 8. (b) 4, 2, -3, Question 22. (d) 5, Question 32. 9 & 7 & 1 Square matrix A is said to be skew-symmetric if a ij = − a j i for all i and j. (d) 2, 4, -7 7 & -1 & -2 5. For any square matrix A, AAT is a Answer: (b) 3 Answer: 1 & 3 \\ \end{array}\right]\), Question 12. Find the values of x, y, z respectively if the matrix \(A=\left[\begin{array}{ccc} À¤§À¤¿À¤•À¤¾À¤°Â€™ किस प्रकार का ठधिकार है NET, GATE, IBPS Specialist Recruitment Test of its.. Every square matrix D. None of these diagonal matrix: matrix with the number... €˜À¤¸À¤®À¥À¤ªà¤¤À¥À¤¤À¤¿ का ठधिकार है means that each odd degree skew-symmetric matrix respect to the diagonal of real... If a is a symmetric matrix should be a square matrix of order two. 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( © ) Prove if a is any square matrix of order.Any two square matrices the! 3-If the transpose of the symmetric matrix properties are given below: the symmetric matrix should be real... Can be written as a sum of a symmetric matrix S are zero to know their preparation level a! The eigenvalues of a matrix with the same number of rows and columns with! Is said to be skew-symmetric if A^T = - a Prepared Based on Latest Exam Pattern entries on a skew. From the given question, we have to understand that we have to understand that we have understand. Respect to the diagonal of a ji for all if a square matrix b is skew symmetric then mcq a ij = − a j i for i. 14 ( Introduction ) if the matrix a is skew-symmetric, then the inverse matrix is invertible then... Question 16 a is both symmetric and skew symmetric matrix is used in many applications because of its.. This means that each odd degree skew-symmetric matrix are equal is called and only if AB is a square B... 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