Thread: What is the Matrix T?

1. What is the Matrix T?

Consider the linear transformation T: R^3->R^3 which acts by rotation around the y-axis by an angle of pi, followed by a shear in the x-direction by a factor of 2.
a) Find the matrix for T. Explain your method.
b) What is T(1,2,3)
c) Without calculation, explain whether the matrix you found in a) is invertible. What is the transformation corresponding to the inverse?

2. Re: What is the Matrix T?

Please show some work in all of your problems so that we get the idea you have actually tried them.

3. Re: What is the Matrix T?

I'll be completely honest, I haven't. I just have no clue what to do.

4. Re: What is the Matrix T?

Originally Posted by BrodyF03
I'll be completely honest, I haven't. I just have no clue what to do.
are you in a class? do you have a textbook?

5. Re: What is the Matrix T?

Yeah, I'm in the class MAT1341 at the University of Ottawa. I do have a textbook, and I've looked through it trying to find a way to find a solution and so far I've been unsuccessful.

6. Re: What is the Matrix T?

Originally Posted by BrodyF03
Yeah, I'm in the class MAT1341 at the University of Ottawa. I do have a textbook, and I've looked through it trying to find a way to find a solution and so far I've been unsuccessful.
it's a pretty straightforward question if you've covered linear transformations at all.

a 3x3 rotation matrix about say the Z axis, of rotation angle $\theta$ is

$R_{\theta}=\left(\begin{array}{ccc}\cos(\theta) &\sin(\theta) &0 \\ -\sin(\theta)&\cos(\theta) &0\\ 0 &0 &1\end{array}\right)$

that sort of thing must be in your book somewhere.

a shear matrix in the Z direction of shear factor $\lambda$ is

$S_{\lambda}=\left(\begin{array}{ccc}1 &0 &0 \\ 0 &1 &0 \\ 0 &0 &\lambda \end{array}\right)$

again that's got to be in your book.

take another look

7. Re: What is the Matrix T?

Thanks for the help, I'm trying to find it but once again I can't haha. I'll keep trying I guess.