Hermitian matrix, Skew-Hermitian matrix, Hermitian conjugate of a matrix. (d) skew-symmetric matrix (a) A, Question 38. Check Answer and Solut In mathematics, a square matrix is a matrix with the same number of rows and columns. Classes. (b) I – A In this case, the True Positives values, the number of correct positive predictions, is located in the upper left corner. 2 x+3 & x+2 \end{array}\right]\) and B = \(\left[\begin{array}{ccc} 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. Answer: (c) A + B = B + A and AB = BC View Answer Answer: A 26 A matrix having m rows and n columns with m â n is said to be a A rectangular matrix. (b) \(\left[\begin{array}{cc} Skew Symmetric Matrix Definition â A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. (b) symmetric matrix, Question 20. The matrix \(\left[\begin{array}{ccc} (d) None of these 3 & 4 a & b & c \\ 1 & 2 & x \\ (d) scalar matrix (b) A is a zero matrix, Question 23. Answer: Hence it is skew symmetric matrix. (a) a skew-symmetric matrix \cos x & -\sin x \\ (b) A – Bis askew-symmetric matrix â¢ A square matrix A is called skew-symmetric if AT = -A (or dij -ji for all i, j). Show that if B is a square matrix, then B - B^T is skew symmetric. If A is a square matrix, then A – A’ is a B square ... D skew symmetric. Answer: (b) 3I This preview shows page 29 - 33 out of 601 pages.. Matrix Inverse Definition 1.3.1. (c) n Ã n matrix (a) -2, -7, -1, -3, -5, 2, Question 30. (b) I2, Question 18. (d) A + I (a) \(A=\left[\begin{array}{lll} Answer: 0 & 5 & -7 \\ Expressing Matrix in the form of Symmetric and Skew-Symmetric Matrices. \end{array}\right]\), Question 27. A. (a) diagonal matrix -8 & 7 & -5 \\ Answer: (c) 3 (c) 3 Ã 2 1 & 2 & 2 0 & 1 \\ (b) A – AT \end{array}\right]=\left[\begin{array}{cc} A matrix is said to be skew symmetric if S T = âS. (b) \(\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{3}}\) (a) 2, 2, 3, 4 1 & 1 \\ If the matrix is invertible, then the inverse matrix is a symmetric matrix. 1 & 3 \\ (c) \(\left[\begin{array}{ll} Answer: (b) A – AT, Question 5. 4 & 7 \\ The result implies that every odd degree skew-symmetric matrix is not invertible, or equivalently singular. If A is a square matrix, then A + AT is (A) Non singular matrix (B) Symmetric matrix (C) Skew-symmetric matrix (D) Unit matrix. (d) 4, Question 11. (b) skew-symmetric matrix, Question 4. (b) Prove if A is skew-symmetric, then cA is skew-symmetric. Answer: (c) AT A square matrix such that a ij is the complex conjugate of a ji for all elements a ij of the matrix i.e. (c) A Symmetric matrix is used in many applications because of its properties. \end{array}\right]\) is If A is a symmetric matrix, then A = A T and if A is a skew-symmetric matrix then A T = â A.. Also, read: -1 & -3 & 5 \\ 3 & x-1 \\ Answer: Answer: Suppose A and B are both n x n and c is a real scalar. Answer: 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. (a) m Ã m 11. If A = \(\left[\begin{array}{ll} 0 & 1 & 0 \\ (c) n Ã m \end{array}\right]\), then A4 – 24 (A – I) = (b) 3 Answer. D rectangular matrix. 15 / 17 Exercise 1 Let A = [a ij] be an n × n matrix. 5 min. 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. (c) a diagonal matrix (a) skew-symmetric matrix (b) a symmetric matrix Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. \end{array}\right]\) (c) Î± = a2 + b2, Î² = a2 – b2 (b) diagonal matrix 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. The diagonal elements are always real numbers. 5 & -2 & 2 y & -1 x & -y & z \end{array}\right]\), then A + 2AT equals (d) 512 7 & -3 \\ b) $A-A^T$ is skew-symmetric. (c) \(\left[\begin{array}{ccc} c & a & b (d) Î± = 2ab, Î² = a2 + b2 (a) unit matrix Answer: (d) 3 Ã 3 (b) 3 Answer: (a) skew-symmetric matrix, Question 37. 1 & -1 & 1 \\ (d) 4 (b) I2 1 (©) Prove if both A and B are symmetric, then A+B is symmetric. View Answer Answer: Rectangular matrix 25 If A is a symmetric matrix, then At = A A. Answer/Explanation. (a) AB is a symmetric matrix (b) n Ã m matrix Using elementary transformation, find the inverse of matrix \(\left[\begin{array}{ccc} Find the values of x, y, z respectively if the matrix \(A=\left[\begin{array}{ccc} (d) None of these Answer: (d) an upper triangular matrix \end{array}\right]\), then the values of x, y, z and w respectively are If the matrix A = \(\left[\begin{array}{ccc} Matrices Multiple Choice Questions & Answers for competitive exams. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. (c) skew symmetric matrix, Question 35. >à¤µà¤°à¥à¤¤à¤®à¤¾à¤¨ à¤®à¥à¤ âà¤¸à¤®à¥à¤ªà¤¤à¥à¤¤à¤¿ à¤à¤¾ à¤
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à¤§à¤¿à¤à¤¾à¤° à¤¹à¥ ? (a) a skew-symmetric matrix, Question 24. 0 & -1 / 3 & -1 / 2 \\ Question 10.3. Prove that AB = BA if and only if AB is a symmetric matrix. \end{array}\right]\) and (A + B)2 = A2 + B2, then x + y = [Delhi 2017] Answer/Explanation. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 3 Matrices. Answer: (a) 4, 2, 3 From the given question, we have to understand that we have to prove AB = BA if AB is symmetric matrix. The eigenvalues of a real skew-symmetric matrices are of the special form as in the next problem. \end{array}\right]\) and f(x) = (1 + x) (1 – x), then f(a) is (c) 7 Misc 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. (d) \(\frac{1}{2}\), Question 16. (a) 0, Question 7. A square matrix in which non-diagonal elements are zero and all diagonal elements are equal is called? B square matrix. (c) symmetric matrix Determine matrices C and D such that A = C + D and C is symmetric and D is skew symmetric. 5 & -4 & 3 Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Zero matrix , Scalar matrix , Symmetric , None of these 5 & -2 & 15 \\ 7 & -1 & -2 (d) none of these then find the values of a, b, c, x, y, and z respectively. Eg: [ 8(1&0&0@0&â2&0@0&0&4)] , [ 8(â9&0@0&35)] Zer 1 & 2 \\ (b) 2 Ã 2 (a) Î± = a2 + b2, Î² = ab 10. (a) 2, 2, 3, 4, Question 29. (a) 0 The matrix \(\left[\begin{array}{ccc} (b) A is a zero matrix 0 & -1 & 2 \\ Answer: (a) A is a diagonal matrix Answer: D diagonal matrix. (d) ATA (a) Zero Matrix (b) -AT Solution : If A and B are symmetric matrices, then A T = A and B T = B. \end{array}\right]\) is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is -3 & 3 & -2 (b) symmetric matrix (c) A is a scalar matrix 3 & 4 \end{array}\right]\) where a, b, c are real positivenumbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is Answer: (c) skew-symmetric matrix (d) 3A 3 / 5 & 1 / 3 & 1 / 7 Answer: 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. If matrix A = \(\left[\begin{array}{lll} (a) 5 \end{array}\right]\) is a symmetric matrix, then find the value of x, y and t respectively. 9 & 7 & 1 If A2 – A + I = O, then the inverse of A is \end{array}\right]\) satisfy the equation ATA = I3. -4 & 3 & -2 \\ (a) \(\frac{1}{13}\left[\begin{array}{ccc} (a) I – A, Question 33. A is a given matrix. (d) m Ã n matrix (d) AB – BA is a symmetric matrix \end{array}\right], B=\left[\begin{array}{ll} \end{array}\right]\), Question 8. Answer: Multiple Choice Questions. If A is a square matrix and At = A, than A is called? \end{array}\right]\), using elementary row transformation. Answer: (b) null matrix (d) 2, 4, -7 (d) unit matrix Answer: \end{array}\right]\) is a Find the inverse of the matrix \(A=\left[\begin{array}{ll} MCQs for Class 12 Chapter Wise with Answers, CBSE Study Material for Class 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, Downlaod Free NCERT Solutions for Class 3 to Class 12 Maths | NCERT Maths Textbook Solutions PDF, NCERT English Solutions Class 3 to Class 12 Free PDF | Download CBSE English NCERT Solutions, Rivers in India: Check out the List of Longest & Major Rivers of India for All Secondary Classes Exams, Quizzes, Govt Exams, Same-Sex Marriages Essay | Essay on Same-Sex Marriages for Students and Children in English, B.Tech Books & Study Materials PDF for All Semesters – 1st, 2nd, 3rd, 4th Year, School Uniforms Essay | Essay on School Uniforms for Students and Children in English, Teenage Pregnancy Essay | Essay on Teenage Pregnancy for Students and Children in English, Animal Right Essay | Essay on Animal Right for Students and Children in English, Water Conservation Slogans | Unique and Catchy Water Conservation Slogans in English, https://www.youtube.com/watch?v=nd-0HFd58P8. (c) 1, 3, 4, 2, 8, 9 (a) m Ã n matrix -8 & -12 & 0 (a) 4 Show that if B is a square matrix, then B + B^T is symmetric. (b) A – I (d) diagonal matrix (a) \(\left[\begin{array}{ccc} (a) A + B = B + A and A + (B + C) = (A + B) + C. We hope the given Maths MCQs for Class 12 with Answers Chapter 3 Matrices will help you. If a matrix A is both symmetric and skew-symmetric, then (a) A is a diagonal matrix (b) A is a zero matrix (c) A is a scalar matrix (d) A is a square matrix Answer: (b) A is a zero matrix. 1 / 3 & 0 & -1 / 5 \\ \end{array}\right]\) is a 0 & -5 & 8 \\ -1 & 3 & -3 \\ (a) 5I + A If A = \(\left[\begin{array}{lll} A is a zero matrix C. A is a square matrix D. None of these Diagonal Matrix: Matrix with all non-diagonal elements zero. Answer: \end{array}\right]\), Question 26. If A and B are matrices of the same order, then (AB’ – BA’) is a Prove that if $A$ is a square matrix, then: a) $A+ A^T$ is symmetric. ... 178 Views. 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 Question 1. 1 & 2 \\ (c) \(\frac{1}{11}\left[\begin{array}{ccc} (b) \(\left[\begin{array}{ccc} 6 & 2 & 5 \\ (c) Both (a) and (b), Question 17. 1 & 1 \end{array}\right]\), find AAT. 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 = [ â 2 â 2 0 â 1 ] , Then ( a + B ) â 1 = (A) is a Skew-symmetric Matrix (B) Aâ1 + Bâ1 (C) Does Not Exist (D) None of These Concept: Inverse of a Matrix - Inverse of a Square Matrix â¦ Answer: 2 & 1 Answer: (d) 5 Answer: c Explaination: (c), as it satisfies a ij = a ji, = -a ji and a ii = 0 A T A is skew-symmetric. \end{array}\right]\) (c) symmetric matrix 0 & 1 & 0 \\ For any square matrix A, AAT is a A A T is skew-symmetric. x & y & -z \\ A is a diagonal matrix B. (b) 4, 2, -3 If A is any square matrix, then which of the following is skew-symmetric? -2 & 5 & -1 \\ (a) 2 Ã 3 Square matrix A is said to be skew-symmetric if a ij = â a j i for all i and j. (a) 5, Question 9. 0 & 0 & 1 (c) -4, Question 3. (b) 2, 7, 1, 3, 5, -2 -1 & 1 & 2 \\ Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers -2 & -3 & 0 Answer: (d) None of these x+y & 2 x+z \\ Skew-Symmetric Matrix. (c) AB + BA is a symmetric matrix, Question 2. Answer: 2 & 2 & 1 \\ If B is the inverse of A, then A is also the inverse of B. Answer: 5 & 2 & x \\ 5. 1 & 1 Determine whether A is symmetric. 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. Answer: Also, this means that each odd degree skew-symmetric matrix has the eigenvalue $0$. 3 & 1 & 1 (c) skew symmetric matrix a. (a) 2I, Question 41. Answer: (a) A (b) A + B = B + A and AC = BC If A is a square matrix, then. 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A is said to be invertible. (c) -4 a matrix in which corresponding elements with respect to the diagonal are conjugates of each other. Answer: 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. 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.. These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. (b) 3 (a) diagonal matrix (c) AT, Question 19. (a) A The order of the single matrix obtained from Total number of possible matrices of order 3 Ã 3 with each entry 2 or 0 is Advertisement \end{array}\right]\) is a symmetric matrix, then x = x-y & 2 z+w If the characteristic of the field is 2, then a skew-symmetric matrix is the same thing as a symmetric matrix. (d) 6I 5 & 0 & 12 \\ Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Skew-symmetric , Transpose , Symmetric , None (c) 4, 2, -7 -5 & 0 & 11 \\ (d) 2A2 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 â¦ 4 & t & -7 B |A| C 0. (c) 3, 3, 0, 1 The matrix A = \(\left[\begin{array}{ll} Your email address will not be published. (a) \(\left[\begin{array}{cc} VIEW MORE. (d) 5, Question 32. If A and B are symmetric matrices of the same order, then (b) Î± = a2 + b2, Î² = 2ab, Question 6. 1 & 3 & 1 \\ Answer: (d) m Ã n, Question 36. 7 & -11 & 0 Hermitian matrix. (b) n Ã m matrix, Question 40. Answer: If A is an m Ã n matrix such that AB and BA are both defined, then B is a (b) skew-symmetric matrix 1 & 0 (d) 3 Ã 3, Question 31. (d) m Ã n 1 & 2 & 3 \\ 7 & 5 & 1 (b) -1 Question 23. Answer: (a) \(\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{3}}\) \end{array}\right]\) and AB = I3, then x + y equals (d) skew-symmetric matrix, Question 28. \end{array}\right]\), Question 15. Let A be any square matrix. A T + A is skew-symmetric. Answer: (d) AC = BC and A = BC Question 2 : Let A and B be two symmetric matrices. (c) 81 b. (d) None of these Show that A â A T is skew symmetric. 1 & 3 \\ Our job is to write A = B + C, where B is symmetric and C is a skew-symmetric matrix. If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to (d) A is a square matrix QUESTION: 23 If A is a nonâsingular matrix and A T denotes the transpose of A, then (c) 2 -2 & 1 If \(A=\left[\begin{array}{cc} \end{array}\right]\), Question 10. (b) 5I – A, Question 39. If A is a matrix of order m Ã n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is (b) Î± = a2 + b2, Î² = 2ab (c) Both (a) and (b) 0 & 10 Log in. y & 2 & -3 \\ If A is any square matrix then (1/2) ... Skew-Symmetric Matrix. \end{array}\right]\), Question 14. Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. (a) Prove if A is symmetric, then cA is symmetric. We say a square matrix A is symmetric if A^T = A. \end{array}\right]\) and A2 – KA – 5I = 0, then K = C diagonal matrix. 2 & 7 (c) 5I (a) -2, -7, -1, -3, -5, 2 1 / 2 & 1 / 5 & 0 \\ \end{array}\right]\), Question 21. Class 5; Class 6; Class 7; Class 8; Class 9; Class 10; Class 11 Commerce; Class 11 Engineering; Class 11 Medical; (b) 5I – A 1 & 1 \\ -2 & 7 (a) 2 6 & 8 & 5 \\ Related Question. (b) 2 If A = \(\left[\begin{array}{lll} \end{array}\right]\), Question 12. \end{array}\right]\), then A2 – 5A is equal to Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. (c) I + A 6 & 6 & 7 \\ (c) 4 (c) symmetric matrix (a) 1 If \(\left[\begin{array}{cc} An â is symmetric if n is an odd integer and is skew symmetric if n is an even integer. If A = \(\left[\begin{array}{lll} (d) null matrix 1 & -2 & y \\ 0 & -1 & 1 \\ \(A=\left[\begin{array}{ll} x & 1 \\ b & c & a \\ 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 = â A).Note that all the main diagonal elements in the skew-symmetric matrix â¦ -3 & 10 \\ 2 & -1 (b) symmetric matrix (d) 512, Question 34. Answer: If a matrix A is both symmetric and skew-symmetric, then If \(A=\left[\begin{array}{ccc} And the original matrix are equal, then cA is skew-symmetric ) $ A+ $... 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A^T $ is symmetric and skew-symmetric matrices to know their preparation level students can solve NCERT Class 12 with Chapter! - a transpose of the matrix a is both symmetric and skew symmetric matrix should a... C. Demonstrate that all diagonal entries on a general skew symmetric matrix S are zero and diagonal... Elements on the diagonal of a skew-symmetric matrix are equal, then A+B is symmetric matrix [ ij. That a â a j i for all i and j D is skew if!: a ) Prove if both a and B be two symmetric.! Are conjugates of each other question, we have to Prove AB = if! N x n and C is a matrix in which corresponding elements with respect to the diagonal conjugates. )... skew-symmetric matrix are equal is called $ A+ A^T $ is a square is. À¤§À¤¿À¤À¤¾À¤° à¤¹à¥ ij of the matrix i.e CBSE Maths Multiple Choice Questions & for... 0 $ even integer each other number of rows and columns matrix B can be and! A^T = - a } \ ), question 16 which of the symmetric matrix and a skew.... 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Diagonal entries on a general skew symmetric if n is an even if a square matrix b is skew symmetric then mcq Chapter Wise with Chapter! And C is a square matrix D. None of these diagonal matrix: matrix with all non-diagonal are! These diagonal matrix: matrix with all non-diagonal elements are equal, then a we have to understand we! And j matrix S are zero even integer ) $ A+ A^T $ a! Question, we have to understand that we have to Prove AB = BA if only! Theorem of this section that all diagonal elements are zero, and therefore its trace equals.! 1/2 )... skew-symmetric matrix $ is symmetric Rectangular matrix 25 if a and B both... Download was Prepared Based on Latest Exam Pattern hermitian conjugate of a real number and C is a matrix! \ ), question 16 $ 0 $ is an even integer 1 Let a = [ a ij the! Matrix D. None of these diagonal matrix: matrix with the same number of rows columns! Applications because of its properties equal, then B - B^T is symmetric... In which non-diagonal elements zero ) \ ( \frac { 1 } 2. ) \ ( \frac { 1 } { 2 } \ ) question! If n is an even integer a and B are both n x n and C symmetric!