Linear Transformation / Coordinate Vector Question

[Gotejjeken]

Homework Statement

The following vectors form an ordered basis E = [v1, v2] of the subspace V = span(v1,v2):

v1 = (1,2,1)^T , v2 = (3,2,1)^T.

The vector v = (24,-8,-4)^T belongs to the subspace V. Find its coordinates (c1,c2)^T = [v]E relative to the ordered basis E = [v1,v2].

Homework Equations

None.

The Attempt at a Solution

I am not quite sure how to approach this problem. I wanted to calculate the inverse of:

1 3
2 2
1 1

and then multiply v = (24, -8, -4)^T by the inverse to get the coordinate vector relative to E, however I have no idea if that is the right approach. I feel I'm missing something...

 

[Mark44]

Homework Statement

The following vectors form an ordered basis E = [v1, v2] of the subspace V = span(v1,v2):

v1 = (1,2,1)^T , v2 = (3,2,1)^T.

The vector v = (24,-8,-4)^T belongs to the subspace V. Find its coordinates (c1,c2)^T = [v]E relative to the ordered basis E = [v1,v2].

Homework Equations

None.

The Attempt at a Solution

I am not quite sure how to approach this problem. I wanted to calculate the inverse of:

1 3
2 2
1 1

The only matrices that have inverses are square matrices. The one you show above is 3 x 2, so isn't square.

and then multiply v = (24, -8, -4)^T by the inverse to get the coordinate vector relative to E, however I have no idea if that is the right approach. I feel I'm missing something...

Solve the equation below for the constants c1 and c2.
(24, -8, -4)^T = c1*(1,2,1)^T + c2*(3,2,1)^T

 

[Gotejjeken]

Oh, wow. Thank you, it seems I was over-complicating things...the wording of that problem had my brain in knots.