Answer
a = 1, b = -1, c = 1. This system has solution which confirms that w is in the subspace spanned by v1, v2, v3.
Work Step by Step
To express w as linear combination of v1, v2, v3. Let a, b, c be the scalars:
Consider av1+bv2+cv3 = w
a[8 -4 -3 9]+b[-4 3 -2 -8]+c[-7 6 -5 -18] = [9 -4 -4 7]
The augmented matrix is : [ 8 -4 -7 9
-4 3 6 -4
-3 -2 -5 -4
9 -8 -18 7 ]
rref(aug) = [ 1 0 0 1
0 1 0 -2
0 0 1 1
0 0 0 0 ]
a = 1, b = -1, c = 1
