Question

Evaluate the determinant for the following matrix: [1 4 4 5 2 2 1 5 5]

(This is a 3x3 matrix)

Answer 1

I would assume the order of the 3×3 matrix to be in this manner:

1 4 4
5 2 2
1 5 5

To determine the determinant of the matrix, you must multiply the number diagonally. For a 3×3 matrix, you must also form 3 diagonals up and 3 diagonals down. To do this, you copy the the first two columns and place it next to the third column.

1 4 4 1 4
5 2 2 5 2
1 5 5 1 5

The sum of the products of the diagonals down is subtracted to the sum of the products of the diagonals up. In other words,
Determinant = ∑(products of diagonal down) - ∑(products of diagonal up)
Determinant = [(1*2*5)+(4*2*1)+(4*5*5)]-[(1*2*4)+(5*2*1)+(5*5*4)]
Determinant = 0

The determinant of the matrix is zero.