WW Chapter 4 Section Problem 9 Previous Problem List Next (1 point) Let u--5 | ,
ID: 3137403 • Letter: W
Question
WW Chapter 4 Section Problem 9 Previous Problem List Next (1 point) Let u--5 | , v = |-| | , and w = | 41 We want to determine if one of [u, v, w] is in the span of the others. To do that we write the vectors as columns of a matrix A and row reduce that matrix. To check this we add row to the second We then add the third We then add row to the new third row We conclude that times the first times the first row to times the new second O A. None of the vectors [u, v, w] is in the span of the others. B. One of the vectors (u, v, w) is in the span of the others. C. We cannot tell if one of the vectors [u, v, w] is in the span of the others.Explanation / Answer
Let A be the matrix with u,v,w as columns. Then A =
-1
-1
5
-5
-1
41
2
5
1
To determine whether one of u,v,w is in the span of the other 2 vectors, we row reduce A as under:
Add -5 times the 1st row to the 2nd row
Add 2 times the 1st row to the 3rd row
Add -3/4 times the new 2nd row to the new 3rd row
Then A changes to
-1
-1
5
0
4
16
0
0
-1
We conclude that u,v,w are linearly independent. Thus none of u,v,w is in the span of the other 2 vectors. Option A.
-1
-1
5
-5
-1
41
2
5
1
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