Question

Linear algebra question: a vector u and a set S are given. If possible, write u as a linear combination of the vectors in S.

u = [3], S = {[1],[2],[-2]}
[8], {[2],[3],[-5]}

Thank you.

Answer 1

1 2 -2 |3
2 3 -5 |8

and augment

Answer 2

Sx = u

x = aug(S|u)

Answer 3

1 2 -2 |3
2 3 -5 |8



1 2 -2 | 3
-1 -3/2 5/2 |-4
----------------
0 1/2 1/2 -1


1 2 -2 | 3
0 1 1 |-2


1 0 -4 | 7
0 1 1 |-2


maybe

x1 4 7
x = x2 = x3 -1 + -2
x3 1 0

Answer 4

with x3 = 0; we can use:

Sx = 7s1 -2s2 + 0s3 = u

Answer 5

I'm a bit confused. How did you figure out to set x3=0?

Answer 6

becasue x3 can be any value; so I simply choose the easiest one for me to use

Answer 7

the row reduction also tells me that I only really need to use the first 2 column vectors so the last ones a but of a useless tagalong

Answer 8

Got it. Thank you.