Find all (a) minors and (b) cofactors of the matrix. Then (c) expand by cofactors to find the determinant. Please show your work. It would help a lot. Thx

Question

[ -6 4 -16 ]

[ -6 -4 12 ]

[ 2 -6 -12 ]

Answer 1

You can use any row or column to find the determinant:

Let's us the first column:

det(A) = -6 |-4 12| - (-6) |4 -16| + 2|4 -16|

|-6 -12| |-6 -12| |-4 12|

det (A) = -6(48+72) + 6(-48-96) + 2(48-64) = -1616

As you go along column (or row), the cofactor matrix consists of all the entries in the matrix not in the row or column of the element in the column you are using. Note that the cofactor is negative if the element's ij product is odd (If you prefer: alternate adding or subtracting starting with 1,1)

Hope that helps.