Linear Transformation Problems
Hello, I require assistance with two LT problems.
1) Given the matrix $\begin{bmatrix} 1 &3 \\ 2 & 1 \end{bmatrix} $ , how would a circle with its center on the origin and r=1 be transformed?
2) Using the following matrix, answer the next questions. A= $\begin{bmatrix} 3 & 4 \\ 3 & 1 \end{bmatrix} $
a) Find the real numbers "a" and "b" given: A$\binom{2}{3} $ =a$\binom{2}{3} $ , A$\binom{2}{1} $ = b$\binom{2}{1} $
b)Find the real numbers "c, d, e and f"given: $\binom{1}{0} $ = c$\binom{2}{3} $ + d$\binom{2}{1} $ , $\binom{0}{1} $ = e$\binom{2}{3} $ + f$\binom{2}{1} $
c) Using the results from a), solve: $A^{n} $ $\binom{2}{3} $, $A^{n} $ $\binom{2}{1} $
d) Using the results from b) and c), solve $A^{n} $
Answer
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I added some more details at the end of the file ( please see the second attachment). This was a challenging problem. Took me a while to write the solutions.

Hey, I know I already accepted the answer, but I have a quick question if you don't mind. In the circle problem, when substituting 'y' on the equation 1, you write x=3((2X+Y)/5)Y. Shouldn't that 'Y' be a "X'? If that is a mistake, I can correct it myself no problem, your methodology is otherwise very clear. If it is not, could you tell me how you got that 'Y'? Thanks for all your help!

Yes, you are right. Sorry for the mistake. It wouldn't change the result much. Just a slightly different formula for the rotated ellipse. I can fix it for you if you like. Please let me know.

Hey, thanks for the response. Its no problem, I already did the correction, but thanks again for your support.

Great! Sorry for my mistake again.
 answered
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