Answer
y = [ -4 -8 6 -5] = -0.2[ 3 8 -5 2]+ -0.4[ -5 7 -8 -2]+ 0.6[ -9 -6 3 -9]
Work Step by Step
To do this, we need to check if there exist scalars c1, c2, c3 such that:
y = c1a1+c2a2+c3a3 where a1, a2, a3 are columns of A.
a1 = [ 3 8 -5 2], a2 = [ -5 7 -8 2], a3 = [ -9 6 -3 -9]
Let's represent this system in augmented matrix form and then row reduce to find the solution:
[ 3 -5 -9 -4
8 7 -6 -8
-5 -8 3 6
2 -2 -9 -5]
rref(aug) = [ 1 0 0 -0.2; 0 1 0 -0.4; 0 0 1 0.6]
c1 = -0.2, c2 = -0.4, c3 = 0.6
This system has a solution which confirms that y is in the subspace spanned by the columns of A. Therefore,
y = [ -4 -8 6 -5] = -0.2[ 3 8 -5 2]+ -0.4[ -5 7 -8 -2]+ 0.6[ -9 -6 3 -9]
