[a, b If A, = |d, e, fil [az bz c Az = |d2 ez fal [az b, cs] Az = [d3 es fsl and are any 2 x 3 matrices, and k and h are real numbers, show that: 9. (A, + A2) + A, = A, + (A2 + A,) 10. (k +h) A, =kA +hA, 11. k (A, +A2) = k A, + kA, 12. k (hA) = (kh) A

[a, b If A, = |d, e, fil [az bz c Az = |d2 ez fal [az b, cs] Az = [d3 es fsl and are any 2 x 3 matrices, and k and h are real numbers, show that: 9. (A, + A2) + A, = A, + (A2 + A,) 10. (k +h) A, =kA +hA, 11. k (A, +A2) = k A, + kA, 12. k (hA) = (kh) A

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 78E

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Question

[a, b
If Aj =
|d, e, f.
[a2 bz c2]
A, =
|d2 ez fl
[az bz c3
A, =
[d3 ez fs]
and
are any 2 x 3 matrices, and k and h are
real numbers, show that:
9. (A, + A2) + A3 = A, + (A2 + A3)
10. (k + h) A, = k A, + h A
11. k (A, + A2) = k A, + kA,
12. k (h A,) = (kh) A3

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