2. Use matrix multiplication to find the orthogonal projection of (1, 2, - 3) onto the a. ху-plane. b. xz-plane.

Suppose A is a 2 × 2 matrix which rotates every vector clockwise by 45degrees . Geometrically, what does A^−1 do to vectors?

Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is translation by (1, 4, 3). To blow up the picture around the center point (1, 4, 3), would you use vST or vT S?

Find the matrix P that multiplies (x, y, z) to give (y, z, x). Find the matrix Q that multiplies (y, z, x) to bring back (x, y, z).