Use a combination of row operations and cofactor expansion t

Use a combination of row operations and cofactor expansion to evaluate the following determinants. |1 4 4 1 -5 5 -1 2 3| |3 1 5 -4 -1 2 -2 1 3| |-1 2 6 0 4 4 5 0 4 6 6 4 4 3 4 2| |2 3 2 -5 3 2 5 2 1 2 4 4 2 -2 4 5| |1 4 4 1 -5 5 -1 2 3| = _______ (Simplify your answer.)

Solution

(A)

Your matrix

Eliminate elements in the 1st column under the 1st element

Eliminate elements in the 2nd column under the 2nd element

Multiply the main diagonal elements

1 x (-9) x 23/3 = -69

Determinant is -69

(B)

Your matrix

Eliminate elements in the 1st column under the 1st element

Eliminate elements in the 2nd column under the 2nd element

Multiply the main diagonal elements

3 x 1/3 x (-37) = -37

Determinant is -37

(C)

Your matrix

Eliminate elements in the 1st column under the 1st element

Eliminate elements in the 2nd column under the 2nd element

Eliminate elements in the 3rd column under the 3rd element

Multiply the main diagonal elements

-1 x 12 x (-23/6) x 80/23 = 160

Determinant is 160

(D)

Your matrix

Eliminate elements in the 1st column under the 1st element

Eliminate elements in the 2nd column under the 2nd element

Eliminate elements in the 3rd column under the 3rd element

Multiply the main diagonal elements

2 x (-5/2) x 17/5 x (-69/17) = 69

Determinant is 69

Sign		A1	A2	A3
+	1	1	4	4
2	1	-5	5
3	-1	2	3