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

7 projection on a different axes question

  • Thread starter nhrock3
  • Start date
  • #1
415
0
7)
[tex]T:R^{2}->R^{2}[/tex] projection transformation on X-axes paralel to the
line
[tex]y=-\sqrt{3}x[/tex]
find the representative matrices of T{*} by B=\{(1,0),(0,1)\} basis
how i tried:
i understood that the x axes stayed the same but the y axes turned
into
[tex]y=-\sqrt{3}x[/tex]
our T takes some vector and returns only the new x part with respect
to the new y axes.
any guidanse?
 

Answers and Replies

  • #2
33,262
4,963
7)
[tex]T:R^{2}->R^{2}[/tex] projection transformation on X-axes paralel to the
line
[tex]y=-\sqrt{3}x[/tex]
find the representative matrices of T{*} by B=\{(1,0),(0,1)\} basis
how i tried:
i understood that the x axes stayed the same but the y axes turned
into
[tex]y=-\sqrt{3}x[/tex]
our T takes some vector and returns only the new x part with respect
to the new y axes.
any guidanse?
If I understand what you're trying to say, then
[tex]T\begin{bmatrix}1 \\ 0\end{bmatrix} = \begin{bmatrix}1\\ 0\end{bmatrix}[/tex]
and
[tex]T\begin{bmatrix}0 \\ 1\end{bmatrix} = k\begin{bmatrix}1\\\sqrt{3}\end{bmatrix}[/tex]

With a little trig you can figure out what k needs to be. What you know what a linear transformation does to a basis, you can write the matrix that represents the transformation.
 

Related Threads for: 7 projection on a different axes question

Replies
1
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
870
  • Last Post
Replies
2
Views
866
Replies
0
Views
1K
  • Last Post
Replies
6
Views
1K
Replies
4
Views
992
Replies
6
Views
5K
Top