HW16: Problem 3 Previous Problem List Next (1 point) a. Write the vector (-9,1,
ID: 3137608 • Letter: H
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HW16: Problem 3 Previous Problem List Next (1 point) a. Write the vector (-9,1, 7) as a linear combination of a (0,-5,-1), a (3,-3,-5) and a -5,-1, 5). Express your answer in terms of the named vectors. Your answer should be in the form 4ai +5a2 +6a, which would be entered as 4a1 5a2 6a3. K-9,1,7-45/4a1+29/8a2-73/8a3 b. Represent the vector (-9, 1,7) in terms of the ordered basis B [(0,-5,-1), (3,-3,-5),(-5,-1,5)3. Your answer should be a vector of the general form . -9,1,7)1s Note: You can earn partial credit on tnis probiem. Preview My Answers Submit AnswersExplanation / Answer
a. Let u = (-9,1,7) and let A = [ a1,a2,a3,u] =
0
3
-5
-9
-5
-3
-1
1
-1
-5
5
7
To determine whether u can be expressed as a linear combination of[ a1,a2,a3, we will reduce A to its RREF as under:
Interchange the 1st row and the 2nd row
Multiply the 1st row by -1/5
Add 1 times the 1st row to the 3rd row
Multiply the 2nd row by 1/3
Add 22/5 times the 2nd row to the 3rd row
Multiply the 3rd row by -15/32
Add 5/3 times the 3rd row to the 2nd row
Add -1/5 times the 3rd row to the 1st row
Add -3/5 times the 2nd row to the 1st row
Then the RREF of A is
1
0
0
-2
0
1
0
2
0
0
1
3
Hence u = (-9,1,7) = -2a1+2a2+3a3.
b. As per part a. above, we have u = (-9,1,7) = -2a1+2a2+3a3 so that the vector(-9,1,7) , in terms of the ordered basis B, i.e. [u]B = < -2,2,3>
0
3
-5
-9
-5
-3
-1
1
-1
-5
5
7
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