QUESTION: I am struggling with keeps my steps in order, I need help to write a system of linear equations represented by the augmented matrix
2 0 5 -14
0 1 -5 12
5 2 0 4
I am to use x, y, and z for my variables.
The above augmented matrix is a way of writing down, explicitly, the matrix equation AX = B, where
A = | 2 0 5 |
| 0 1 -5 |
| 5 2 0 |
X = | x |
| y |
| z |
B = | -14 |
| 12 |
| 4 |
So AX = B is
| 2 0 5 | | x | = | -14 |
| 0 1 -5 | | y | | 12 |
| 5 2 0 | | z | | 4 |
where matrix multiplication now gives us the set of linear simultaneous equations,
2x + 5z = -14
y - 5z = 12
5x + 2y = 4