8. Given the matrix B =1 111 11Which of the following matrices solves X in the matrix cquation X + I3 = 2(X – B)?2 3 33 2 21 2 2(2 1 1(а) |3 2 3(b) 2 3 2(c) 2 1 2(d) |1 2 13 3 22 2 32 2 11 1 29. Which of the following values of k satisfics the following matrix equation?( 1(k)(k 1 1)1 00 2 -31= 0.1(a) 2(b) 1(c) 0(d) –110. The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal entricsof A. If X and Y are n-by-n matrices, which of the following is a true statement?(a) tr(X²) = [tr(X)]².(b) If tr(X) = 0, then X = 0,.(c) tr(XY) = tr(X)tr(Y).(d) tr(XY) = tr(YX).

Answered: Image /qna-images/answer/ef9b282d-d7b3-45fe-86d3-dff6cd2d00a5.jpg

8. Given the matrix B = |1 1 1 1 1 1 Which of the following matrices solves X in the matrix equation X + I3 = 2(X – B)? (2 3 3 (3 2 2 (1 2 2) (2 1 1) (а) |3 2 3 (b) 2 3 2 (c) |2 1 2 (d) |1 2 1 3 3 2 2 2 3 2 2 1 1 1 2

8. Given the matrix B = |1 1 1 1 1 1 Which of the following matrices solves X in the matrix equation X + I3 = 2(X – B)? (2 3 3 (3 2 2 (1 2 2) (2 1 1) (а) |3 2 3 (b) 2 3 2 (c) |2 1 2 (d) |1 2 1 3 3 2 2 2 3 2 2 1 1 1 2

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 29E

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Question

8. Given the matrix B =
1 1
1
1 1
1
Which of the following matrices solves X in the matrix cquation X + I3 = 2(X – B)?
2 3 3
3 2 2
1 2 2
(2 1 1
(а) |3 2 3
(b) 2 3 2
(c) 2 1 2
(d) |1 2 1
3 3 2
2 2 3
2 2 1
1 1 2
9. Which of the following values of k satisfics the following matrix equation?
( 1
(k)
(k 1 1)1 0
0 2 -3
1
= 0.
1
(a) 2
(b) 1
(c) 0
(d) –1
10. The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal entrics
of A. If X and Y are n-by-n matrices, which of the following is a true statement?
(a) tr(X²) = [tr(X)]².
(b) If tr(X) = 0, then X = 0,.
(c) tr(XY) = tr(X)tr(Y).
(d) tr(XY) = tr(YX).

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