Write a system of linear equations represented by the augmented matrix

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.

Answer 1

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