# Coordinates and change of base

## The Attempt at a Solution

I don't understand where 2v1 + 3v2
and
4v1 - 3v2

came from.

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I see that the vectors are raised to T which I'm pretty sure means they're transposed but that still doesn't get me anywhere.

DryRun
Gold Member
Where's Figure 3.29a? You should post the whole example to help us get a clearer picture of the problem.

HallsofIvy
Homework Helper
You are solving the equations
$$x= \begin{bmatrix}11 \\ 7\end{bmatrix}= a\begin{bmatrix}1 \\ 2\end{bmatrix}+ b\begin{bmatrix}3 \\ 1\end{bmatrix}$$
which is the same as the two equations a+ 3b= 11 and 2a+ b= 7. Can you solve for a and b?
And
$$y= \begin{bmatrix}-5 \\ 5\end{bmatrix}= c\begin{bmatrix}1 \\ 2\end{bmatrix}+ d\begin{bmatrix}3 \\ 1\end{bmatrix}$$
which is the same as the two equations c+ 3d= -5 and 2c+ d= 5. Can you solve for a and b?

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ok, thanks, I got it now.