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College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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In Exercises 1 and 2, compute each matrix sum or product if it is
defined. If an expression is undefined, explain why. Let
A =
C =
2 0 -1
-5 2
4
-2]
12
-[
[43]
1
1. -2A, B - 2A, AC, CD
3. Let A =
B =
A =
D =
17
4 -1
[2]
5
5 -2
[₁
7 -5 1
-4 -3
3
-1
5
1
4
2. A + 2B, 3CE, CB, EB
In the rest of this exercise set and in those to follow, you should
assume that each matrix expression is defined. That is, the sizes
of the matrices (and vectors) involved "match" appropriately.
Compute 312 - A and (31₂) A.
4 Compute A - 513 and (513) A, when
9 -1 3
-8
7 -6
-4
18
-5
=[-]
3
E =
In Exercises 5 and 6, compute the product AB in two ways: (a) by
the definition, where Ab, and Ab₂ are computed separately, and
(b) by the row-column rule for computing AB.
10
11
Transcribed Image Text:In Exercises 1 and 2, compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let A = C = 2 0 -1 -5 2 4 -2] 12 -[ [43] 1 1. -2A, B - 2A, AC, CD 3. Let A = B = A = D = 17 4 -1 [2] 5 5 -2 [₁ 7 -5 1 -4 -3 3 -1 5 1 4 2. A + 2B, 3CE, CB, EB In the rest of this exercise set and in those to follow, you should assume that each matrix expression is defined. That is, the sizes of the matrices (and vectors) involved "match" appropriately. Compute 312 - A and (31₂) A. 4 Compute A - 513 and (513) A, when 9 -1 3 -8 7 -6 -4 18 -5 =[-] 3 E = In Exercises 5 and 6, compute the product AB in two ways: (a) by the definition, where Ab, and Ab₂ are computed separately, and (b) by the row-column rule for computing AB. 10 11
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