Coordinates and change of base

[robertjford80]

Homework Statement

The Attempt at a Solution

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

came from.

 

[robertjford80]

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]

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

 

[HallsofIvy]

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?

 

[robertjford80]

ok, thanks, I got it now.