For each A, B, C below, determine whether {A, B, C} is is linearly independent or linearly dependent. If it is dependent, give a non- trivial linear combination of the matrices yielding the zero matrix. -2 B = -2 7 = 1 -4 -2 7 1 a) A = C = -1 1 4 -7 {A, B, C} is linearly dependent 0 = 0 -2 -10 6 B : 0 -2 - b) A = C = %3D -1 1 5 -3 -2 {A, B, C} is linearly independent

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
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For each A, B, C below, determine whether {A, B, C} is is linearly
independent or linearly dependent. If it is dependent, give a non-
trivial linear combination of the matrices yielding the zero matrix.
1 -2
2 7
-2 7
C =
a) A =
B =
-1 1
1 -4
4 -7
{A, B, C} is linearly dependent
0 = 0
5 -2
-10 6
0 - 2
b) A =
B =
=
C =
%3D
-1 1
5 0
-3 -2
{A, B, C} is linearly independent
Transcribed Image Text:For each A, B, C below, determine whether {A, B, C} is is linearly independent or linearly dependent. If it is dependent, give a non- trivial linear combination of the matrices yielding the zero matrix. 1 -2 2 7 -2 7 C = a) A = B = -1 1 1 -4 4 -7 {A, B, C} is linearly dependent 0 = 0 5 -2 -10 6 0 - 2 b) A = B = = C = %3D -1 1 5 0 -3 -2 {A, B, C} is linearly independent
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