1 2 39. The matrix A =4 5 6 may be written as S +T, where S is a symmetric matrix and T is a7 8 9skew-symmetric matrix. Which of these matrices is equal to S-T?(1 4 7)(c) 2 5 81591 -5 914 -7(a) 2 6 7(b) 2-7(d)34 83693.

Answered: Image /qna-images/answer/77676207-f209-42b1-9c42-78c37ff37dc1.jpg

(1 2 3 45 6 may be written as S+7, where S is a symmetric matrix and T is a 7 8 9 9. The matrix A skew-symmetric matrix. Which of these matrices is equal to S-T? (1 4 7) (c) 2 5 8 159 -5 9 4 -7 (a) 2 6 7 (b) 2 -7 (d) -2 348 -3 369 3 -6 9

(1 2 3 45 6 may be written as S+7, where S is a symmetric matrix and T is a 7 8 9 9. The matrix A skew-symmetric matrix. Which of these matrices is equal to S-T? (1 4 7) (c) 2 5 8 159 -5 9 4 -7 (a) 2 6 7 (b) 2 -7 (d) -2 348 -3 369 3 -6 9

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.3: Inverses Of Matrices And Matrix Equations

Problem 1E

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Question

1 2 3
9. The matrix A =4 5 6 may be written as S +T, where S is a symmetric matrix and T is a
7 8 9
skew-symmetric matrix. Which of these matrices is equal to S-T?
(1 4 7)
(c) 2 5 8
159
1 -5 9
1
4 -7
(a) 2 6 7
(b) 2
-7
(d)
34 8
369
3.

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Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A. Must it be true that A=D?
a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving that if A is an nn symmetric matrix with positive eigenvalues, then there exists a symmetric matrix B such that B2=A.

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