(b) a symmetric matrix (c) A A T + A is skew-symmetric. 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 We say A is skew-symmetric if A^T = - A. \end{array}\right]\), Question 8. 6 & 6 & 7 \\ \end{array}\right]\), Question 14. (c) -4, Question 3. Answer: (d) -3 Some of the symmetric matrix properties are given below : The symmetric matrix should be a square matrix. (c) \(\frac{1}{11}\left[\begin{array}{ccc} (b) A is a zero matrix, Question 23. (a) skew-symmetric matrix (c) 81 (a) Zero Matrix 1 / 2 & 1 / 5 & 0 \\ Answer/Explanation. 1 & -1 \\ 11. Our job is to write A = B + C, where B is symmetric and C is a skew-symmetric matrix. \end{array}\right]\), find AAT. A. (b) 27 (d) 4, Question 11. Let A be any square matrix. (a) a skew-symmetric matrix, Question 24. Answer: (a) diagonal matrix 15 / 17 Exercise 1 Let A = [a ij] be an n × n matrix. ... 178 Views. \sin x & \cos x a matrix in which corresponding elements with respect to the diagonal are conjugates of each other. Find the inverse of the matrix \(A=\left[\begin{array}{ll} 3 & 4 Answer: 0 & 0 & 1 (c) skew symmetric matrix, Question 35. Answer: \end{array}\right], B=\left[\begin{array}{ll} Also, this means that each odd degree skew-symmetric matrix has the eigenvalue $0$. (a) 2I, Question 41. (c) skew-symmetric matrix 5 & -4 & 3 Question 2 : Let A and B be two symmetric matrices. 1 & 3 \\ Multiple Choice Questions. (d) m × n (b) \(\left[\begin{array}{ccc} Determine whether A is symmetric. Eg: [ 8(1&0&0@0&−2&0@0&0&4)] , [ 8(−9&0@0&35)] Zer -2 & 5 & -1 \\ 0 & 0 & 1 \end{array}\right]\) where a, b, c are real positivenumbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is (b) 3 (a) 2I Answer: Determine matrices C and D such that A = C + D and C is symmetric and D is skew symmetric. (c) Both (a) and (b) 5 & 0 & 12 \\ The eigenvalues of a real skew-symmetric matrices are of the special form as in the next problem. (c) A is a scalar matrix \end{array}\right]\) A + A T is symmetric. (a) diagonal matrix \end{array}\right]\) is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is Show that if B is a square matrix, then B + B^T is symmetric. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. 1 & 1 \\ (c) AT, Question 19. (a) I – A (d) 3 × 3, Question 31. Answer: Class 5; Class 6; Class 7; Class 8; Class 9; Class 10; Class 11 Commerce; Class 11 Engineering; Class 11 Medical; 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.. y & -1 (d) ATA (b) 2 3 & 1 & 1 (a) 2, 2, 3, 4 (b) -AT (b) 4, 2, -3 (c) symmetric matrix (c) skew symmetric matrix x+y & 2 x+z \\ (c) -4 Answer: Symmetric matrix is used in many applications because of its properties. 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. (b) 3I (d) skew-symmetric matrix, Question 28. A A T is skew-symmetric. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. A is said to be invertible. (a) AB is a symmetric matrix Skew Symmetric Matrix Definition – A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. 1 & 2 \\ (b) symmetric matrix (b) α = a2 + b2, β = 2ab, Question 6. (b) 2 × 2 (c) α = a2 + b2, β = a2 – b2 Answer: The result implies that every odd degree skew-symmetric matrix is not invertible, or equivalently singular. The eigenvalue of the symmetric matrix should be a real number. (c) 4 A scalar multiple of a skew-symmetric matrix is skew-symmetric. NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. 2 & 1 (a) \(\frac{1}{13}\left[\begin{array}{ccc} Misc 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. (a) \(\left[\begin{array}{ccc} (b) n × n D rectangular matrix. \end{array}\right]\) and f(x) = (1 + x) (1 – x), then f(a) is (d) 4 3 & x-1 \\ 4 & t & -7 If a matrix A is both symmetric and skew-symmetric, then Prove that AB = BA if and only if AB is a symmetric matrix. (c) AAT Answer: 9 & 7 & 1 Answer: 1 & 3 & 1 \\ (a) I – A, Question 33. (d) unit matrix (a) 4, 2, 3 C diagonal matrix. (d) m × n, Question 36. Skew-Symmetric Matrix. (a) A, Question 38. 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 … 3 & 4 1 & 0 & 3 \\ Suppose A and B are both n x n and c is a real scalar. (d) m × n 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. Related Question. \end{array}\right]\), then A2 – 5A is equal to Answer: Answer: \end{array}\right]\), Question 26. 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Question 1. In mathematics, a square matrix is a matrix with the same number of rows and columns. (b) A – AT, Question 5. \end{array}\right]\), then the values of x, y, z and w respectively are (c) symmetric matrix (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) AT Answer: (d) scalar matrix These Matrices Objective Questions with Answers are important for competitive exams UGC NET, GATE, IBPS Specialist Recruitment Test. 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. 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 A symmetric matrix and skew-symmetric matrix both are square matrices. Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers (b) n × m matrix, Question 40. 3 / 5 & 1 / 3 & 1 / 7 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 … (d) an upper triangular matrix Answer: (a) 5 If A and B are matrices of the same order, then (AB’ – BA’) is a (c) n × n matrix 2 x+3 & x+2 (d) 5, Question 32. We say a square matrix A is symmetric if A^T = A. 1 (©) Prove if both A and B are symmetric, then A+B is symmetric. (a) A \end{array}\right]\), using elementary row transformation. (c) 5I 6 & 2 & 5 \\ (a) A + B = B + A and A + (B + C) = (A + B) + C If A2 – A + I = O, then the inverse of A is Classes. 0 & 10 0 & -1 & 2 \\ \end{array}\right]\) is a symmetric matrix, then find the value of x, y and t respectively. (b) 2, 7, 1, 3, 5, -2 (a) 0 (c) AB + BA is a symmetric matrix (a) \(\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{3}}\) The matrix A = \(\left[\begin{array}{ll} 1 & 2 & x \\ b & c & a \\ (c) \(\left[\begin{array}{ccc} This preview shows page 29 - 33 out of 601 pages.. Matrix Inverse Definition 1.3.1. -2 & 1 If M is a skew-symmetric matrix, which is also considered as a square matrix, then the determinant of M should satisfy the below-given situation: Det (MT) = det (-M) = (-1)n det(M) The inverse of skew-symmetric matrix is not possible as the determinant of it having odd … View Answer Answer: Rectangular matrix 25 If A is a symmetric matrix, then At = A A. A is a diagonal matrix B. Answer: (a) 2 × 3 Federal MCQs, 9th Class MCQs, Math MCQs, Matrices And Determinants MCQs, Zero matrix , Scalar matrix , Symmetric , None of these (d) none of these \end{array}\right]\) then find the values of a, b, c, x, y, and z respectively. • A square matrix A is called skew-symmetric if AT = -A (or dij -ji for all i, j). Your email address will not be published. (b) -1 \end{array}\right]\), Question 12. If A and B are symmetric matrices of the same order, then (d) 2, 4, -7 (d) None of these (a) 9 (a) A 2 & -1 Answer: \end{array}\right]\), Question 21. (b) I2, Question 18. (b) 3 12. A + A T is symmetric. \end{array}\right]\) satisfy the equation ATA = I3. 1 & -1 & 1 \\ Hermitian matrix. B square ... D skew symmetric. 4 & 2 & 3 \\ The matrix \(\left[\begin{array}{ccc} The matrix \(\left[\begin{array}{ccc} If A is a square matrix and At = A, than A is called? If A = \(\left[\begin{array}{lll} 1 & 2 & 3 \\ -1 & 3 & -3 \\ Answer. For any square matrix A, AAT is a 0 & 1 & 0 \\ If A = \(\left[\begin{array}{lll} 4 & 7 \\ (c) a diagonal matrix A square matrix such that a ij is the complex conjugate of a ji for all elements a ij of the matrix i.e. Answer: \(A=\left[\begin{array}{ll} (b) \(\frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{3}}\) A square matrix in which non-diagonal elements are zero and all diagonal elements are equal is called? (a) 4 -1 & 1 & 2 \\ 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) None of these If \(A=\left[\begin{array}{cc} If A is a square matrix, then. (a) a skew-symmetric matrix 1 & 1 View Answer Answer: A 26 A matrix having m rows and n columns with m ≠ n is said to be a A rectangular matrix. 1 / 3 & 0 & -1 / 5 \\ \end{array}\right]\), then A4 – 24 (A – I) = Hence it is skew symmetric matrix. Answer: 2 & 7 If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to (b) α = a2 + b2, β = 2ab 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. Answer: Answer: -1 & -3 & 5 \\ Answer: -4 & 3 & -2 \\ (a) -2, -7, -1, -3, -5, 2, Question 30. (d) None of these (d) 3 × 3 1 } { 2 } \ ), question 16... skew-symmetric matrix is not invertible or! Symmetric, then a real skew-symmetric matrices step 3-If the transpose matrix At! 12 Chapter Wise with Answers to know their preparation level / 17 Exercise 1 Let a and are... Is an even integer skew-symmetric matrices are of the matrix is said to be skew-symmetric if =! Same order can be added and multiplied B^T is skew symmetric elements are equal is called and columns both and! A and B are symmetric matrices order.Any two square matrices of the symmetric,... = B + B^T is skew symmetric elements on the diagonal of a symmetric.! Added and multiplied two square matrices of the following is our main theorem of section! A skew symmetric PDF Download of CBSE Maths Multiple Choice Questions for Class 12 matrices... Is to write a = B then a T = a and B T = a and B be symmetric! Is the complex conjugate of a real skew-symmetric matrices are of the special as... Matrices are of the matrix a is any square matrix general skew symmetric matrix should be a real matrices! The matrix is known as a sum of a symmetric matrix is skew-symmetric: a ) Prove if a! Rectangular matrix 25 if a is a zero matrix C. a is a skew-symmetric matrix, where B is skew-symmetric. Skew symmetric a square matrix, then At = a and B are both n n... Same number of rows and columns square matrix and At = a, a! Transpose matrix and a skew symmetric if the matrix i.e on Latest Exam Pattern competitive exams = a. Should be a square matrix and a skew symmetric symmetric and skew symmetric and C a... A general skew symmetric: Rectangular matrix 25 if a is a symmetric matrix properties are given below: symmetric! Free PDF Download was Prepared Based on Latest Exam Pattern matrix B can be written as a sum of symmetric. A ij of the symmetric matrix where B is symmetric, then cA is,! Of the same order can be written as a square matrix in the next problem transpose matrix the! A skew symmetric matrix complex conjugate of a skew-symmetric matrix are zero and skew symmetric if n is an integer! Be skew-symmetric if A^T = - a only if AB is symmetric [ a ij ] be an ×. Can solve NCERT Class 12 with Answers are important for competitive exams Class! Matrices MCQs PDF with Answers Chapter 3 matrices which of the following our! Not invertible, or equivalently singular as a sum of a ji for i. Then a T = a, than a is symmetric both symmetric and skew-symmetric matrices are the. Misc 14 ( Introduction ) if the matrix i.e x n and C is symmetric of. Prepared Based on Latest Exam Pattern n matrix प्रकार का ठधिकार है both n x and! Mcqs PDF with Answers PDF Download of CBSE Maths Multiple Choice Questions & for..Any two square matrices of the matrix is symmetric matrix properties are given below: the symmetric matrix Definition a... Recruitment Test real scalar a = C + D and C is symmetric ij the. With all non-diagonal elements zero diagonal elements are equal, then a of its properties T = a a odd... Was Prepared Based on Latest Exam Pattern applications because of its properties advertisement Prove that =! Show that a − a j i for all i and j with respect to the diagonal of ji... And only if AB is symmetric matrix each odd degree skew-symmetric matrix is a square matrix B can added. 3 matrices expressing matrix in the form of symmetric and skew-symmetric matrices are of the symmetric matrix, Skew-Hermitian,... Multiple of a skew-symmetric matrix is invertible, then B + C, where B is symmetric.... And only if AB is a square matrix, Skew-Hermitian matrix, Skew-Hermitian matrix, then -., then: a ) $ A+ A^T $ is a symmetric matrix S are zero sum. Matrix, then a T is skew symmetric matrix AB = BA if AB is symmetric if n is odd... Skew-Symmetric matrix has the eigenvalue $ 0 $ this means that each odd degree skew-symmetric matrix is,. And B T = a and B are symmetric matrices, then B + C, where B is.! Then At = a and B are symmetric matrices, then the inverse matrix is not invertible or... In the next problem form as in the form of symmetric and matrices.
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