Find a solution to the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.

Question

Find a solution to the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.

a.		c.
b.		d.

 

Please select the best answer from the choices provided

A

B

C

D

Answer 1

Finding the correct answer here is important, but perhaps equally important is finding it using the method of matrix reduction, since those are the instructions.

The augmented matrix is

4 -2 -5 -51

4 -1 -2 -36

4 -2 4 -24

You'll have to forgive the poor formatting. This answer box doesn't have a proper math symbol editor.

Using elementary row operations, the reduced row echelon form of the augmented matrix is

1 0 0 -6

0 1 0 6

0 0 1 3

from which we conclude that the system has a unique solution (-6,6,3).

Answer 2

Subtract third equation from first.

-9z = -27

x = 3

The only triple containing z = 3 is A.

You can verify x and y

Answer 3

I added the "like terms"=12x-5y-3z=-111

substitute (-6,6,3) got -111