Lecture Notes

quiz-style questions:

• Write down a linear transformation that takes $x^2/4+y^2=1$ to the unit circle. Is it unique? (which means: Is there more than one such linear transformation? )
• Write down a linear transformation that takes the line $x=y$ to $x=0$. Is it unique?
• Let $M=\begin{bmatrix} 0 & 1 \cr -1 & 0 \end{bmatrix}$. Compute $M^2, M^3, M^4$.