# Express a as a linear combination of b and c

1. Jun 16, 2009

### Gregg

1. The problem statement, all variables and given/known data

$a=\left( \begin{array}{c} -1 \\ 3 \\ 13 \end{array} \right)$

$b=\left( \begin{array}{c} 1 \\ 2 \\ 2 \end{array} \right)$

$c=\left( \begin{array}{c} 1 \\ 3 \\ 5 \end{array} \right)$

3. The attempt at a solution

Am I supposed to determine this from inspection or through a process?

2. Jun 16, 2009

### Gregg

a=-6b+5c from simultaneous eqautions its sorted.

3. Jun 16, 2009

### MLeszega

There is a process you can do to solve this (although some of these problems are easy enough to be solved through inspection). You want to write a as a linear combination of b and c, so write it like this:

x$$\vec{b}$$ + y$$\vec{c}$$ = $$\vec{a}$$

Then you solve for x and y. This can be done easily by creating a matrix and putting it in RREF.

Your matrix should look like this:

1 1 : -1
2 3 : 3
2 5 : 13

So use Gaussian elimination, put it in RREF and you will have your answers for x and y. (Sorry about the sad looking matrix but I suck with latex lol)