HW 10 (1) ((2 points) Use Laplace expansion along the 2nd row to compute the a 2 b determinant of the matrix 7 -2 For what values of a, b is this 7 -3 matrix invertible? (Hint: use Theorem 6.2.4 in text book.) (2) (2 points) Let A, B denote two invertible 4 x 4 matrices. Suppose that B is obtained from A by performing the following list of elementary row operations on A: interchange the first and third rows; multiply the second row by 2; add 2 times the fourth row to the second row; multiply the second row by T. Suppose that det(A) = v2. Then compute det(B). (Hint: use Theorem 6.2.3 in text book.) (3) (2 points) Let T : R2 - R2 denote the linear transformation which satisfies r( [ ] ] - [ ] and r([ : ]> = [2]. Compute the determinant of T. (Hint: use Definition 6.2.11 in the text book.) (4) (4 points) A, B denote two n x n matrices which satisfy det(A) = v5 and det(B) = -2. Use Theorem 6.2.6 and 6.2.8 in our text book to carry out the following computations. (a) det (A2 B-1) =? (b) det(A3 BA-1B4A-2B3) =? (Hint: for each positive integer n we have An = (A-])" if A is invertible.)