1. ## Matrices/Determinant problem

Okay, so I had to row reduce the matrix below to upper-triangular form in order to find the determinant.

[0, 0, 2, 0, 0]
[2, 0, 58, 96, -1]
[2, 1, 58, 96, -1]
[0, 0, 2, -1, 0]
[1, 0, 58, 96, 2]

Row-reducing it to upper-triangular form, I wound up with:
[1, 0, 29, 48, -1/2]
[0, 1, 0, 0, 0]
[0, 0, 1, 0, 0]
[0, 0, 0, 1, 0]
[0, 0, 0, 0, 3/2]

I know that to calculate the determinant of an n by n upper-triangular matrix, all you do is multiply the entries along the diagonal. However, when I found the determinant of the first matrix using cofactors, I got -10. Multiplying the entries along the diagonal of the row-reduced upper triangular form, I got 3/2. Am I doing something wrong here? I've done out the row-reduction several times, and I keep getting a determinant of 3/2.

2. Originally Posted by buckaroobill
Okay, so I had to row reduce the matrix below to upper-triangular form in order to find the determinant.

[0, 0, 2, 0, 0]
[2, 0, 58, 96, -1]
[2, 1, 58, 96, -1]
[0, 0, 2, -1, 0]
[1, 0, 58, 96, 2]

Row-reducing it to upper-triangular form, I wound up with:
[1, 0, 29, 48, -1/2]
[0, 1, 0, 0, 0]
[0, 0, 1, 0, 0]
[0, 0, 0, 1, 0]
[0, 0, 0, 0, 3/2]

I know that to calculate the determinant of an n by n upper-triangular matrix, all you do is multiply the entries along the diagonal. However, when I found the determinant of the first matrix using cofactors, I got -10. Multiplying the entries along the diagonal of the row-reduced upper triangular form, I got 3/2. Am I doing something wrong here? I've done out the row-reduction several times, and I keep getting a determinant of 3/2.
The determinant of this matrix is -10.

Review what happens as you reduce the matrix to upper triangular form in
the light of what is in the attachment to this post.

RonL