pls. answer 5 and 6

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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pls. answer 5 and 6

4. In the matrix equation MAT = H, M and T are square matrices. If H is a 2-by-3 matrix, what is
the size of matrix A?
(a) 3-by-2
(b) 3-by-3
(c) 2-by-3
(d) 2-by-2
1 (1
Which of the following equals A4?
1
5. Consider the matrix A
V2
-1
(a)
-1)
-1)
1
(Ь)
V2 1
(c)
1
(d)
2-1 -1
-1
-1
6. Let A and B be n-by-n matrices. Which of the following conditions is sufficient to conclude that
АВ — ВА?
(a) A+ B = B+A.
(b) (АB)? — АР В?.
(с) А? — В? — (А + B)(А — В).
(d) (A+ B)² = A² + B².
|3D
Transcribed Image Text:4. In the matrix equation MAT = H, M and T are square matrices. If H is a 2-by-3 matrix, what is the size of matrix A? (a) 3-by-2 (b) 3-by-3 (c) 2-by-3 (d) 2-by-2 1 (1 Which of the following equals A4? 1 5. Consider the matrix A V2 -1 (a) -1) -1) 1 (Ь) V2 1 (c) 1 (d) 2-1 -1 -1 -1 6. Let A and B be n-by-n matrices. Which of the following conditions is sufficient to conclude that АВ — ВА? (a) A+ B = B+A. (b) (АB)? — АР В?. (с) А? — В? — (А + B)(А — В). (d) (A+ B)² = A² + B². |3D
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