## COMMENTS ON QUIZ #8

**
1. **

(a) D is the (orthogonal) projection of the vector
3
1
2

on the column space of A.

(b) One multiplies by the transpose of A (A^T),
which is

1 0 1
2 1 0

2.

(a) 2(1) - 3(5) = 2-15 = -13

(b) Expanding with respect to the first row gives
three terms that are 0 and

3 0 0
-2 det 7 1 0
97 11 5

(the sign associated with the fourth entry of the first
row is - ; the pattern is + - + - ).

The determinant of the lower triangular matrix is (3)(1)(5),
the product of the diagonal entries, and so the original
determinant is -2(15) = -30.

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**