Solve Linear Combination: Matrices Problem x1...x6 = [4,0,2]

[Derill03]

x1[0,0,0] + x2[1,1,0] + x3[0,1,0] + x4[-1,-1,0] + x5[0,0,1] + x6[1,0,-1] = [4,0,2]

** left to right is top to bottom **


I am first asked to find 3 columns that span R3, I found that [-1,-1,0],[0,0,1],[1,0,-1] span r3 because they have a non-zero determinant. Now the next question is where i have trouble

I am asked to express the right side as a linear combination of the three columns i chose?

How can i write the three columns as a linear combination? I haven't been able to find any really good explanation of a linear combination, can ne one help?

 

[CompuChip]

It just means, find three numbers a, b, c such that
a [-1, -1, 0] + b [0, 0, 1] + c [1, 0, -1] = [4, 0, 2]

The left hand side is called a linear combination of [-1, -1, 0], [0, 0, 1] and [1, 0, -1].

 

[Derill03]

ok then if I've done this correctly it should be:

0*[-1,-1,0] + 6*[0,0,1] + 4*[1,0,-1] = [4,0,2]

a=0
b=6
c=4