# Linear algebra-linear combination

## Homework Statement

For each matrix, can you write the third column of the matrix as a linear combination
of the first two columns?

$$\left[ \begin{array}{cccc} 1 & 2 & 3 \\ 7 & 8 & 9 \\ 4 & 5 & 6 \end{array} \right]$$

x=a(U1)+b(U2)

## The Attempt at a Solution

I let x equal the third column, U1 as the first column, and U2 as the second column. I solved the augmented matrix and got:

$$\left[ \begin{array}{cccc} 1 & 0 & -1 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array} \right]$$

which a=-1, b=2.

This where I'm confused. Do I just multiply a by the first column and b by the second then that will give me a matrix that is the linear combination wrt the third column?

Related Calculus and Beyond Homework Help News on Phys.org
A linear combination of x and y is a*x + b*y. So you want to know if you can find some a and b such that
a*first column + b*second column is equal to third column.

Can you?

HallsofIvy