1 Let A be the matrix 4 5 3 1 A 1 1 2 2 1 1 a Compute det A

1. Let A be the matrix 4 5 3 1 A- 1 1 2 2 1 1 (a) Compute det (A) using the second row. (b) Compute det (A) using the third column

Solution

a) det(A) using the second row

==> det(A) = -1[5(1) - 1(3)] +1[4(1) - 2(3)] - 2[4(1) - 2(5)]

==> det(A) = -2 + (-2) - 2(-6) = -2 - 2 + 12

==>det(A) = 8

b) det(A) using third column

det(A) = 3[1(1) -2(1)] -2[1(4) -2(5)] + 1[1(4) -1(5)]

==> det(A) = 3(-1) -2(-6) + 1(-1) = -3 + 12 -1 = 8