• Support PF! Buy your school textbooks, materials and every day products Here!

Coordinates and change of base

  • #1

Homework Statement


Screenshot2012-05-12at100357PM.png




The Attempt at a Solution



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

came from.
 

Answers and Replies

  • #2
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.
 
  • #3
DryRun
Gold Member
838
4
Where's Figure 3.29a? You should post the whole example to help us get a clearer picture of the problem.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
955
You are solving the equations
[tex]x= \begin{bmatrix}11 \\ 7\end{bmatrix}= a\begin{bmatrix}1 \\ 2\end{bmatrix}+ b\begin{bmatrix}3 \\ 1\end{bmatrix}[/tex]
which is the same as the two equations a+ 3b= 11 and 2a+ b= 7. Can you solve for a and b?
And
[tex]y= \begin{bmatrix}-5 \\ 5\end{bmatrix}= c\begin{bmatrix}1 \\ 2\end{bmatrix}+ d\begin{bmatrix}3 \\ 1\end{bmatrix}[/tex]
which is the same as the two equations c+ 3d= -5 and 2c+ d= 5. Can you solve for a and b?
 
Last edited by a moderator:
  • #5
ok, thanks, I got it now.
 

Related Threads on Coordinates and change of base

  • Last Post
Replies
3
Views
807
  • Last Post
Replies
20
Views
2K
  • Last Post
Replies
11
Views
3K
Replies
1
Views
1K
Replies
8
Views
5K
Replies
9
Views
619
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
6
Views
3K
Replies
9
Views
4K
Replies
2
Views
2K
Top