Homework for Diagonalizing Matrices

1. (DiagonalPractice) This easy exercise only requires that students know how to multiply matrices. It can be assigned before the concept of diagonalization is introduced and then used as an early lecture example.

Perform the following matrix multiplications:

$$\frac{1}{\sqrt{2}}\pmatrix{1&1\cr1&-1}\quad \pmatrix{3&1\cr1&3}\quad \frac{1}{\sqrt{2}}\pmatrix{1&1\cr1&-1}$$

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