is also symmetric. More generally, if C is an m× n matrix, its transpose, CT, is a n× m matrix. (a) Explain why each of A², A3, etc. (Hint: if you are stuck, look back at Example 20.3.6.) In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space. Solution. Thus, any symmetric matrix must be diagonalizable.) for all indices and .. Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. If A is a square matrix, then show that (a) (A + AT) is symmetric matrix. MATH 54 TRUE/FALSE QUESTIONS FOR MIDTERM 2 SOLUTIONS PEYAM RYAN TABRIZIAN 1. The product AAT is always symmetric. On the other hand, if the number of eigenvectors is the same as the size of the matrix, then this is true. Question 1 : Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix: Misc 5 Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric. Let A be a square matrix. (a) alse.F orF example, A= [0 1 0 0]. Let us look into some problems to understand the concept. Then, we can write. COMEDK 2005: If A is a square matrix.such that A3 = 0, then (I + A)-1 is (A) I - A (B) I - A-1 (C) I - A + A2 (D) I + A + A2. (d) The eigenvector matrix Sof a symmetric matrix is symmetric. C. If A is skew symmetric, then A3 is symmetric. then CT = 7 −3 4 1 2 4!. Suppose A is an n x n symmetric matrix. (A= PDP 1, so A3 = PD3P= PeDePe1, where Pe= Pand De= D3, which is diagonal) (b) TRUE If Ais a 3 3 matrix with 3 (linearly independent) Note that whereas C is a 3× 2 matrix, its transpose, CT, is a 2× 3 matrix. If A is a symmetric matrix, then AT is also symmetric. D. If A is symmetric, then A + A2 is symmetric. B. E. The sum A + AT is always symmetric. If A and B are matrices of same order, then (AB’ – BA’) is a A. skew symmetric matrix B. null matrix C. symmetric matrix D. unit matrix asked Sep 18 in Matrices by Shyam01 ( 50.3k points) matrices Any square matrix can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix. A symmetric n × n A matrix always has n distinct real eigenvalues. (a) TRUE If Ais diagonalizable, then A3 is diagonalizable. FALSE( - They need not be distinct) A quadratic form has no cross-product terms if and only if the matrix of the quadratic form is a diagonal matrix. If A is a matrix of order m x n and B is a matrix of order n x p then the order of AB is: [ a b c ] is a (b) (A- A') is skew symmetric (c) (AAT) is symmetric matrix plss helpp someone urgentlyyy class 12 matrix Transcript. C. Consider the linear system x + 2y + 3z = a 2x − y + z = b Check Answer and Solu Exercise 24.4. 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