I have this textbook "Mathematics for 3D Game Programming & Computer Graphics" and Chapter on matrices starts from a linear algebra perspective. They have this example problem of a linear system that that go through and reduce to canonical form using an algorithm. I have been going over it again and again and I cannot come up with the same answer they get in the book for one operation in a particular element. The weird thing is the rest of the operations end up with the right solution for the system.
I'll repro the work here:
Given system: 3x + 2y - 3z = -13 4x - 3y + 6z = 7 x - z = -5
| 3 2 -3 | -13 | | 4 -3 6 | 7 | | 1 0 -1 | -5 |
First swap rows one and two and multiply new row 1 by 1/4:
My problem is with the -25/17 in element 1,4 The operation there should be ( -2/3 * -73/17 ) + 7/4 unless I am wrong. But then how could the answer be negative? The answer I get is 941/204 but using this does not ultimately solve the system. I'll show work below but the last steps with their data: