math question?

Question

Solve each system of equations using matrices. If the system has no solution, say it is inconsistent.

{ 2x + y - z = 2
{ x + 3y + 2z = 1
{ x + y + z = 2

Can you explain how you solve this so I understand?

The solution of the system in the appendix is x = 2 and y = -1 and z = 1

Answer 1

Find Delta, the determinant of the system.

|2 1 - 1|
| 1 3 2| =6 + 2 - 1 +3 - 1 - 4 = 5, which is different from 0
| 1 1 1 |

If Delta is different from 0, then you have a solution and it's unique.

Find delta x, delta y and delta z and find x, y and z dividing deltax by delta, etc.

Deltax is calculated this way:
|2 1 - 1|
|1 3 2| =6 + 4 - 1 +6 - 1 - 4 = 10, so x = 2
|2 1 1 |

Observe that I substituted the first column by the results of the equations, then the second column to find deltay and, finally, the third column to find deltaz
Deltay is calculated this way:
|2 2 - 1|
|1 1 2|
|1 2 1 |

Deltaz is calculated this way:
|2 1 2|
|1 3 1|
|1 1 2 |

Answer 2

There really isn't room here to explain the theory of matrices and determinants. But type in 'linear equations' and you'll get a ton of sites that talk about them and explain how they work. There are even some that have 'matrix calculators' that will make that problem real easy ☺

Doug