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.