Gauss Jordan inverse matrix, row of all zeros

Question

I'm using the Gauss Jordan method to find the inverse of this matrix: [ 2 4 10; 3 4 6; 4 4 2]

So, I set up this matrix on the left and the identity matrix on the right, and I reduce until I get the identity matrix on the left. However, for this specific matrix, I get a row of all zeros for the last row (instead of '0, 0, 1') and the last column is '-4, 9/2, 0' instead of ' 0, 0, 1'.

Why did this happen? What does this mean? And how does this relate to the determinant or condition number of the matrix?

Answer 1

It's not an invertible matrix. The determinant is zero.