For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. Give your combination as an expression using u, v, and w for the vector variables , 7, and . 3 W-2 3 1 -3 a) = -1 7= 3 2 -5 (, , } is linearly independent 2 4 0 b) = -2 V = 1 w=10 -2 -2 4 {u, , } is linearly dependent 0=0

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Chapter5: Inner Product Spaces
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For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors
yielding the zero vector. Give your combination as an expression using u, v, and w for the vector variables , 7, and .
3
w=-2
3
1
-3
a) = -1 7= 3
2
-5
(, , } is linearly independent
2
4
0
b) = -2 V = 1 w=10
-2
-2
4
{u, 7, w} is linearly dependent
0=0
Transcribed Image Text:For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. Give your combination as an expression using u, v, and w for the vector variables , 7, and . 3 w=-2 3 1 -3 a) = -1 7= 3 2 -5 (, , } is linearly independent 2 4 0 b) = -2 V = 1 w=10 -2 -2 4 {u, 7, w} is linearly dependent 0=0
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