Express a as a linear combination of b and c

[Gregg]

Homework Statement

[itex]a=\left(
\begin{array}{c}
-1 \\
3 \\
13
\end{array}
\right)[/itex]

[itex]b=\left(
\begin{array}{c}
1 \\
2 \\
2
\end{array}
\right)[/itex]

[itex]c=\left(
\begin{array}{c}
1 \\
3 \\
5
\end{array}
\right)[/itex]

The Attempt at a Solution

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

 

[Gregg]

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

 

[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[tex]\vec{b}[/tex] + y[tex]\vec{c}[/tex] = [tex]\vec{a}[/tex]

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)