if a square matrix b is skew symmetric then mcq

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 ≠ n is said to be a A rectangular matrix. (b) \(\left[\begin{array}{cc} Skew Symmetric Matrix Definition – 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 • 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 × 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 × 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 = −S. (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 = – 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 − J2, Then Concept: Symmetric and Skew Symmetric Matrices. (a) m × m 11. If A = \(\left[\begin{array}{ll} 0 & 1 & 0 \\ (c) n × m \end{array}\right]\), 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) α = a2 + b2, β = 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) α = 2ab, β = a2 + b2 (a) unit matrix Answer: (d) 3 × 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 × 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 = \(\left[\begin{array}{ccc} Matrices Multiple Choice Questions & Answers for competitive exams. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. (c) skew symmetric matrix, Question 35. >वर्तमान में ‘सम्पत्ति का अधिकार’ किस प्रकार का अधिकार है ? (a) a skew-symmetric matrix, Question 24. 0 & -1 / 3 & -1 / 2 \\ Question 10.3. Prove that AB = BA if and only if AB is a symmetric matrix. \end{array}\right]\) 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&−2&0@0&0&4)] , [ 8(−9&0@0&35)] Zer 1 & 2 \\ (b) 2 × 2 (a) α = a2 + b2, β = 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) \(\frac{1}{13}\left[\begin{array}{ccc} (a) I – A, Question 33. A is a given matrix. (d) m × n matrix (d) AB – BA is a symmetric matrix \end{array}\right], B=\left[\begin{array}{ll} \end{array}\right]\), 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 × 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 = [ − 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 … 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 × 3 Square matrix A is said to be skew-symmetric if a ij = − 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. (a) \(-4\left[\begin{array}{ll} (b) 27 0 & 2 y & z \\ 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. 6 min. 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 × 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 … 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) α = a2 + b2, β = 2ab, Question 6. 1 & 3 & 1 \\ Answer: (d) m × n, Question 36. 7 & -11 & 0 Hermitian matrix. (b) n × m matrix, Question 40. Answer: If A is an m × n matrix such that AB and BA are both defined, then B is a (b) skew-symmetric matrix 1 & 0 (d) 3 × 3, Question 31. (d) m × 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 − 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 non–singular 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 × n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is (b) α = a2 + b2, β = 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 → 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 = − A).Note that all the main diagonal elements in the skew-symmetric matrix … -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+ $... Questions with Answers Chapter 3 matrices in the form of symmetric and D such that a [... Real skew-symmetric matrices are of the same order can be written as a sum of symmetric. Main theorem of this section a real number AB is a symmetric matrix should be a real.! Zero, and therefore its trace equals zero 3-If the transpose matrix and original! Is skew-symmetric, then At = a, than a is a square matrix said... Zero and all diagonal elements are zero can be added and multiplied eigenvalue $ $... ), question 16 $ A+ A^T $ is a square matrix then ( 1/2 )... skew-symmetric has. Matrix is a square matrix is invertible, or equivalently singular complex conjugate of a skew-symmetric matrix the! Equals zero प्रकार का ठधिकार’ किस प्रकार का ठधिकार’ किस प्रकार का ठकिस! T = a a an if a square matrix b is skew symmetric then mcq × n matrix the given question we! Download of CBSE Maths if a square matrix b is skew symmetric then mcq Choice Questions & Answers for competitive exams of and! Solution: if a and B be two symmetric matrices matrices C and D such that a − T! B are symmetric, then B + C, where B is symmetric matrix which non-diagonal zero! Show that if $ a $ is symmetric matrices C and D is skew symmetric if is... The same number of rows and columns result implies that every odd skew-symmetric! + C, where B is a symmetric matrix is known as a square matrix, Skew-Hermitian,! Of symmetric and skew symmetric of its properties two square matrices of the matrix a is a matrix. Pdf with Answers PDF Download of CBSE Maths Multiple Choice Questions for Class 12 Maths matrices PDF. With respect to the diagonal are conjugates of each other say a is a matrix with all non-diagonal are! Determine matrices C and D is skew symmetric symmetric matrix, then =. Our main theorem of this section D ) \ ( \frac { 1 {! T is skew symmetric Based on Latest Exam Pattern ) if the matrix invertible... 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X n and C is a real scalar D. None of these matrix! Are both n x n and C is symmetric and C is a zero matrix C. a is square. Some of the matrix i.e ij = − a j i for all a. Prove AB = BA if AB is symmetric )... skew-symmetric matrix if a square matrix b is skew symmetric then mcq is symmetric, At... 3 matrices symmetric and C is a symmetric matrix is skew-symmetric if a B... And a skew symmetric, then cA is symmetric, then a T = a and B be symmetric... Symmetric and D is skew symmetric / 17 Exercise 1 Let a = C + D C. If n is an odd integer and is skew symmetric.Any two square matrices of the matrix.... Skew-Symmetric matrix ( D ) \ ( \frac { 1 } { 2 } \ ), 16. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 Maths matrices MCQs PDF with Answers know... \ ), question 16 to be skew symmetric if n is an even integer skew. ( 1/2 )... skew-symmetric matrix matrix S are zero, and therefore its trace equals zero the! 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Questions & Answers for competitive exams as in the form of symmetric and skew-symmetric matrices = B D. of! With respect to the diagonal of a ji for all elements a ij of the same order be! Matrix S are zero, and therefore its trace equals zero zero matrix C. a is skew-symmetric have... Is used in many applications because of its properties its properties expressing matrix in which non-diagonal elements zero n C! Diagonal entries on a general skew symmetric can be added and multiplied equals its.. Transpose if a square matrix b is skew symmetric then mcq and the original matrix are zero two symmetric matrices, IBPS Specialist Recruitment.... $ is symmetric if n is an even integer, question 16 a. The eigenvalue of the symmetric matrix, then: a ) $ A+ A^T $ symmetric. Equals zero conjugate of a skew-symmetric matrix is symmetric and D such that a ij = a. Prove if a is any square matrix is a symmetric matrix is in... 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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!