/Math203 Spring 1718/ECW 3/1/key- MATHEMATICAL ASSOCIATION OF AMERICA K webwork/
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/Math203 Spring 1718/ECW 3/1/key- MATHEMATICAL ASSOCIATION OF AMERICA K webwork/ math203 spring1718 / ecw-3/ 1 ECW-3: Problem 1 Problem List Next 1 pointy Are the vectors linearly dependent 5 2 . 4 3 2 and 41 22 -7 inearly independent? If they are linearly dependent, find scalars that are not make the equation below true. all zero such that the equation below is true. they are linearty independent,find the only scalars that wil Note: In order to get crealt for this problem all answers must be correct 1 time You have 2 attempts remaining.Explanation / Answer
Let A = [u,v,w] =
5
4
41
2
3
22
-3
2
-7
To determine whether the vectors u, v, w are linearly independent or not, we will reduce A to its RREf as under:
Multiply the 1st row by 1/5
Add -2 times the 1st row to the 2nd row
Add 3 times the 1st row to the 3rd row
Multiply the 2nd row by 5/7
Add -22/5 times the 2nd row to the 3rd row
Add -4/5 times the 2nd row to the 1st row
Then the RREF of A is
1
0
5
0
1
4
0
0
0
It implies that w = 5u+4v or, 5u+4v-w = 0. Hence, the vectors u, v, w are linearly dependent.
5
4
41
2
3
22
-3
2
-7
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