Linear algebra

(11 points) Our goal is to find the determinant of the matrix A below. Please follow the instructions. Note that the result of each part is used in the next part. 7 -25 11 4 -6 0 9 -7 A = 18 -15 -12 -9 -5 45 8 3 a. b. c. Divide the 2nd column by 5. How is the determinant of this new matrix related to det(A)? Divide the 3rd row of the matrix in (a) by-3. How is the determinant of this new matrix related to det(A)? Keep the 1 in column 2 of the matrix in (b) and use row operations to turn the other entries in column 2 into zeroes. How is the determinant of this new matrix related to det(A)? Perform a cofactor expansion on the matrix from (c) using column 2, then complete the computation of the determinant of A using row operations to obtain a triangular matrix (you are free to decide if you prefer an upper or lower triangular matrix). Do NOT use the 3 x 3 determinant formula, or further cofactor expansions. Show how you completed the calculation. Do not just use a graphing calculator without a solution. d