Let A 0 5 6 1 2 1 4 8 2 We can find the determinant of A by

Let A = [0 5 6 1 2 1 -4 -8 -2]. We can find the determinant of A by using row reduction: First we swap the first and second rows to get [1 2 1 0 5 -6 -4 8 -2]. By what factor does this change the determinant? ____________ Next we multiply the first row by 4 to get [4 8 4 0 5 -6 -4 -8 -2]. By what factor does this change the determinant? ___________ Finally we replace the third row by the sum of itself and the first row to get [4 8 4 0 5 -6 0 0 2] By what factor does this change the determinant? ____________ Since the determinant of the row reduced matrix is _________ the determinant of A is ___________.

Solution

Interchange the 1st row and the 2nd row:

Add 4 times the 1st row to the 3rd row:

Multiply the 2nd row by 1/5:

Multiply the 3rd row by 1/2:

det(A) (-1) (1/5) (1/2) = det(B).

Since det(B) = 1 , we have,

det(A) = -10.

1 2 1 0 5 6 -4 -8 -2