Question

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

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.