Symmetric matrix is used in many applications because of its properties. (a) Zero Matrix (a) skew-symmetric matrix, Question 37. 0 & 0 & 1 Answer: Our job is to write A = B + C, where B is symmetric and C is a skew-symmetric matrix. b & c & a \\ If A and B are symmetric matrices of the same order, then If A is a square matrix, then A + AT is (A) Non singular matrix (B) Symmetric matrix (C) Skew-symmetric matrix (D) Unit matrix. Log in. Answer: -2 & 7 If A = \(\left[\begin{array}{ll} Question 10.3. 2 x+3 & x+2 If B is the inverse of A, then A is also the inverse of B. These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. (d) skew-symmetric matrix, Question 28. (b) 5I – A, Question 39. 2 & -1 Misc 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. If the matrix is invertible, then the inverse matrix is a symmetric matrix. (b) 2, 7, 1, 3, 5, -2 (a) 1 \end{array}\right]\) and AB = I3, then x + y equals Answer: 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¦ 2 & 7 \cos x & -\sin x \\ (a) 2 1 & 0 & 3 \\ (d) scalar matrix A is a diagonal matrix B. 0 & 1 \\ (a) 5, Question 9. (a) 2I, Question 41. (b) Prove if A is skew-symmetric, then cA is skew-symmetric. 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: 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. Answer: Eg: [ 8(1&0&0@0&â2&0@0&0&4)] , [ 8(â9&0@0&35)] Zer Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Zero matrix , Scalar matrix , Symmetric , None of these (d) 6I 2 & 2 & 1 \\ Answer: (b) \(\left[\begin{array}{ccc} The following is our main theorem of this section. If A = \(\left[\begin{array}{ll} \end{array}\right]\), Question 8. (d) 3A 12. Answer: 9 & 7 & 1 NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. 1 & 2 & 3 \\ Find the values of x, y, z respectively if the matrix \(A=\left[\begin{array}{ccc} 0 & 2 y & z \\ Skew-Symmetric Matrix. If the characteristic of the field is 2, then a skew-symmetric matrix is the same thing as a symmetric matrix. A T A is skew-symmetric. Answer: (b) 2 Ã 2 View Answer Answer: A 26 A matrix having m rows and n columns with m â n is said to be a A rectangular matrix. (b) symmetric matrix, Question 20. Solution : If A and B are symmetric matrices, then A T = A and B T = B. \end{array}\right]\), then the values of x, y, z and w respectively are (d) diagonal matrix Hermitian matrix, Skew-Hermitian matrix, Hermitian conjugate of a matrix. 6 & 6 & 7 \\ \end{array}\right]\), then A + 2AT equals (d) None of these If \(A=\left[\begin{array}{cc} (d) Î± = 2ab, Î² = a2 + b2 (d) -1, 3, -2, -7, 4, 5 1 & 2 & 2 1 & 2 \\ (d) an upper triangular matrix If A = \(\left[\begin{array}{lll} We say a square matrix A is symmetric if A^T = A. Answer: (a) -2, -7, -1, -3, -5, 2, Question 30. (b) -AT Using elementary transformation, find the inverse of matrix \(\left[\begin{array}{ccc} (d) 512 \end{array}\right]\) 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. -1 & -3 & 5 \\ -8 & -12 & 0 (c) -2I Multiple Choice Questions. -3 & 3 & -2 \end{array}\right]\) and f(x) = (1 + x) (1 – x), then f(a) is 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. Class 5; Class 6; Class 7; Class 8; Class 9; Class 10; Class 11 Commerce; Class 11 Engineering; Class 11 Medical; Answer: Answer: 4 & t & -7 Matrices Multiple Choice Questions & Answers for competitive exams. 4 & 7 \\ Answer: 1 & 1 \\ A matrix is said to be skew symmetric if S T = âS. and the required skew-symmetric matrix is. \end{array}\right]\) is a symmetric matrix, then find the value of x, y and t respectively. (c) n Ã n matrix Answer: QUESTION: 23 If A is a nonâsingular matrix and A T denotes the transpose of A, then (b) 2 Determine whether A is symmetric. 5 & -2 & 15 \\ 1 / 3 & 0 & -1 / 5 \\ (d) none of these \end{array}\right]\), Question 12. Answer: (b) n Ã m matrix, Question 40. \end{array}\right]\) and B = \(\left[\begin{array}{ccc} 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. 1 / 2 & 1 / 5 & 0 \\ (c) \(\left[\begin{array}{ll} A is said to be invertible. From the given question, we have to understand that we have to prove AB = BA if AB is symmetric matrix. (a) A + B = B + A and A + (B + C) = (A + B) + C Answer: 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. \sin x & \cos x (b) Î± = a2 + b2, Î² = 2ab y & 2 & -3 \\ (a) 5 c & a & b (a) m Ã n matrix (c) A Answer: a matrix in which corresponding elements with respect to the diagonal are conjugates of each other. (c) 1, 3, 4, 2, 8, 9 If A is a square matrix and At = A, than A is called? Hermitian matrix. A is a given matrix. If A = \(\left[\begin{array}{lll} (b) I2 Find the inverse of the matrix \(A=\left[\begin{array}{ll} For any square matrix A, AAT is a A scalar multiple of a skew-symmetric matrix is skew-symmetric. (a) A, Question 38. 3 / 5 & 1 / 3 & 1 / 7 Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers 1 & 0 (a) diagonal matrix 10. Answer: 7 & -11 & 0 Answer: If A is any square matrix, then which of the following is skew-symmetric? 3 & 4 5 & 0 & 12 \\ then find the values of a, b, c, x, y, and z respectively. (c) A is a scalar matrix (a) A + AT (d) 3 Ã 3 B square ... D skew symmetric. (a) 5I + A (b) A – AT Determine matrices C and D such that A = C + D and C is symmetric and D is skew symmetric. 0 & 1 & 0 \\ \end{array}\right]\) satisfy the equation ATA = I3. 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. 1 & -1 & 1 \\ (a) \(-4\left[\begin{array}{ll} [Delhi 2017] Answer/Explanation. (a) Î± = a2 + b2, Î² = ab 1 & 1 \\ 0 & 0 & 1 (d) \(\frac{1}{2}\), Question 16. 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à¤§à¤¿à¤à¤¾à¤° à¤¹à¥ ? (a) \(\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{3}}\) The matrix A = \(\left[\begin{array}{ll} (a) \(\frac{-1}{11}, \frac{2}{11}\), Question 13. If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to (c) I + A Show that if B is a square matrix, then B + B^T is symmetric. -4 & 3 & -2 \\ (b) A + B = B + A and AC = BC (a) I – A (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. (c) symmetric matrix Answer: 1 & 3 & 1 \\ (d) m Ã n (d) AB – BA is a symmetric matrix 0 & 1 & 0 \\ 5. x-y & 2 z+w -8 & 7 & -5 \\ Answer: Suppose A and B are both n x n and c is a real scalar. The order of the single matrix obtained from Prove that AB = BA if and only if AB is a symmetric matrix. A symmetric matrix and skew-symmetric matrix both are square matrices. (b) n Ã m matrix This preview shows page 29 - 33 out of 601 pages.. Matrix Inverse Definition 1.3.1. (d) None of these If A is an m Ã n matrix such that AB and BA are both defined, then B is a The eigenvalue of the symmetric matrix should be a real number. (c) 7 \end{array}\right]\), Question 14. \end{array}\right]\), Question 25. \end{array}\right]\), using elementary row transformation. 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. (b) diagonal matrix a & b & c \\ 6 & 8 & 5 \\ View Answer Answer: Rectangular matrix 25 If A is a symmetric matrix, then At = A A. A + A T is symmetric. (b) A – Bis askew-symmetric matrix 1 (©) Prove if both A and B are symmetric, then A+B is symmetric. Answer: (c) skew symmetric matrix x+y & 2 x+z \\ (a) A (a) 2I 11. (b) 4, 2, -3, Question 22. Answer: If the matrix A = \(\left[\begin{array}{ccc} (c) A + B = B + A and AB = BC x & 1 \\ B |A| C 0. If A2 – A + I = O, then the inverse of A is (c) AB + BA is a symmetric matrix, Question 2. (c) n Ã m Expressing Matrix in the form of Symmetric and Skew-Symmetric Matrices. (d) 5, Question 32. Answer: (b) skew-symmetric matrix, Question 4. (c) 3 Ã 2 (d) None of these (b) null matrix \end{array}\right]\), Question 15. Show that if B is a square matrix, then B - B^T is skew symmetric. Answer: (b) A is a zero matrix 2 & 1 If \(A=\left[\begin{array}{cc} 1 & 1 (c) 2 -2 & -3 & 0 (c) skew symmetric matrix, Question 35. Step 3-If the transpose matrix and the original matrix are equal , then the matrix is symmetric. (a) a skew-symmetric matrix We say A is skew-symmetric if A^T = - A. The matrix \(\left[\begin{array}{ccc} A. (d) 5 Answer: (c) \(\frac{1}{11}\left[\begin{array}{ccc} Answer: c Explaination: (c), as it satisfies a ij = a ji, = -a ji and a ii = 0 \(A=\left[\begin{array}{ll} If A is any square matrix then (1/2) ... Skew-Symmetric Matrix. C diagonal matrix. (a) 4, 2, 3 (b) -1 (b) symmetric matrix D diagonal matrix. Question 23. \end{array}\right]\) is a \end{array}\right]\) and A2 – KA – 5I = 0, then K = (a) A is a diagonal matrix Answer: -1 & 3 & -3 \\ (a) unit matrix (c) AAT Skew Symmetric Matrix Definition â A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. (c) 4, 2, -7 (b) 3I 5 & 2 & x \\ \end{array}\right], B=\left[\begin{array}{ll} D rectangular matrix. Prove that every square matrix B can be written as a sum of a symmetric matrix and a skew symmetric matrix. Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Skew-symmetric , Transpose , Symmetric , None -5 & 0 & 11 \\ (b) I – A The diagonal elements are always real numbers. (c) skew-symmetric matrix (d) 4, Question 11. 3 & x-1 \\ (c) 3, 3, 0, 1 \end{array}\right]\) is a (b) 3 If a matrix A is both symmetric and skew-symmetric, then (d) 512, Question 34. (a) -2, -7, -1, -3, -5, 2 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. (d) m Ã n, Question 36. If \(A=\left[\begin{array}{ccc} Classes. (b) \(\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{3}}\) (b) 2, 3, 1, 2 \end{array}\right]\), Question 21. 0 & -1 & 1 \\ (c) symmetric matrix 1 & -1 \\ The matrix \(\left[\begin{array}{ccc} Your email address will not be published. â¢ A square matrix A is called skew-symmetric if AT = -A (or dij -ji for all i, j). 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¦ If \(\left[\begin{array}{cc} Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. (a) \(\left[\begin{array}{ccc} \end{array}\right]=\left[\begin{array}{cc} It is denoted by A-1. (c) -4 (b) 3 0 & -5 & 8 \\ (a) A 5 min. x & y & -z \\ The sum of two skew-symmetric matrices is skew-symmetric. \end{array}\right]\), then A2 – 5A is equal to (b) 27 (d) None of these Answer: (b) \(\left[\begin{array}{cc} c. Demonstrate that all diagonal entries on a general skew symmetric matrix S are zero. (a) a skew-symmetric matrix, Question 24. (c) \(\left[\begin{array}{ccc} (c) symmetric matrix (c) AT, Question 19. 1 & -2 & y \\ \end{array}\right]\), Question 26. Answer: Answer: Question 2 : Let A and B be two symmetric matrices. \end{array}\right]\) and (A + B)2 = A2 + B2, then x + y = If A = \(\left[\begin{array}{lll} A square matrix such that a ij is the complex conjugate of a ji for all elements a ij of the matrix i.e. If A is a matrix of order m Ã n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is Answer. 3 & 1 & 1 (a) 4 Answer: 1 & 1 \end{array}\right]\), Question 27. y & -1 (d) m Ã n matrix (c) 3 Hence it is skew symmetric matrix. (c) 4 (d) 2, 4, -7 (c) AT \end{array}\right]\) Let A be any square matrix. Question 1. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 3 Matrices. A square matrix in which non-diagonal elements are zero and all diagonal elements are equal is called? (d) 3 Ã 3, Question 31. \end{array}\right]\) where a, b, c are real positivenumbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is \end{array}\right]\) is a symmetric matrix, then x = Total number of possible matrices of order 3 Ã 3 with each entry 2 or 0 is (b) I2, Question 18. Step1: finding transpose of A. Step2: calculating \(A+A^{T}\) Step3: Calculating \(A-A^{T}\) So our required symmetric matrix is. (d) ATA (d) 2A2 3 & 4 (c) Î± = a2 + b2, Î² = a2 – b2 Show that A â A T is skew symmetric. The eigenvalues of a real skew-symmetric matrices are of the special form as in the next problem. (b) 5I – A (a) 2 Ã 3 Prove that if $A$ is a square matrix, then: a) $A+ A^T$ is symmetric. B square matrix. (a) 0 15 / 17 Exercise 1 Let A = [a ij] be an n × n matrix. Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. (a) \(\frac{1}{13}\left[\begin{array}{ccc} 4 & 2 & 3 \\ 7 & 5 & 1 If A is a square matrix, then A – A’ is a 1 a ij = i 2 + j 2 2 a ij = i 2-j 2 2 A square matrix is said to be skew-symmetric if A T = - A. b) $A-A^T$ is skew-symmetric. 7 & -3 \\ \end{array}\right]\) is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is (b) A – AT, Question 5. 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In this case, the True Positives values, the number of correct positive predictions, is located in the upper left corner. (c) 81 (c) a diagonal matrix In mathematics, a square matrix is a matrix with the same number of rows and columns. Answer: (c) -4, Question 3. 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. -1 & 1 & 2 \\ (a) diagonal matrix VIEW MORE. Answer: \end{array}\right]\), then A4 – 24 (A – I) = Answer/Explanation. Answer: Check Answer and Solut (a) AB is a symmetric matrix (a) unit matrix \end{array}\right]\), find AAT. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Answer: (b) Î± = a2 + b2, Î² = 2ab, Question 6. 0 & 10 Answer: \end{array}\right]\), Question 10. (c) Both (a) and (b), Question 17. (d) unit matrix A A T is skew-symmetric. (b) A is a zero matrix, Question 23. (b) a symmetric matrix Related Question. 0 & -1 / 3 & -1 / 2 \\ x & -y & z An â is symmetric if n is an odd integer and is skew symmetric if n is an even integer. Square matrix A is said to be skew-symmetric if a ij = â a j i for all i and j. (c) Both (a) and (b) 1 & 3 \\ (d) null matrix If \(\left[\begin{array}{ll} (b) 4, 2, -3 The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. Answer: 1 & 3 \\ 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: (b) A – I (d) A is a square matrix (a) 9 Answer: (b) n Ã n Also, this means that each odd degree skew-symmetric matrix has the eigenvalue $0$. Answer: (a) 2, 2, 3, 4 (b) symmetric matrix 0 & 5 & -7 \\ 6 min. A + A T is symmetric. -2 & 5 & -1 \\ (a) Prove if A is symmetric, then cA is symmetric. The result implies that every odd degree skew-symmetric matrix is not invertible, or equivalently singular. (a) skew-symmetric matrix (c) AB + BA is a symmetric matrix 0 & -1 & 2 \\ (a) 0, Question 7. (d) AC = BC and A = BC If A and B are matrices of the same order, then (AB’ – BA’) is a (a) \(\left[\begin{array}{cc} (d) 4 6 & 2 & 5 \\ -2 & 1 (d) skew-symmetric matrix 1 & 2 \\ (a) \(A=\left[\begin{array}{lll} 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.. 1 & 2 & x \\ If A is a square matrix, then. (d) None of these (a) I – A, Question 33. a. (c) 5I (a) 2, 2, 3, 4, Question 29. 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. 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