Express a as a linear combination of b and c

[Gregg]

Homework Statement

a=\left(<br /> \begin{array}{c}<br /> -1 \\<br /> 3 \\<br /> 13<br /> \end{array}<br /> \right)

b=\left(<br /> \begin{array}{c}<br /> 1 \\<br /> 2 \\<br /> 2<br /> \end{array}<br /> \right)

c=\left(<br /> \begin{array}{c}<br /> 1 \\<br /> 3 \\<br /> 5<br /> \end{array}<br /> \right)

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\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)