solve system of equations using row operations on augmented matrix

Hey guys I really need some help on solving 2 algebra problems.

The question states: Solve the system of equations using row operations on the augmented matrix.

Problem 1.

x+y-z=5

x+2y-3z=9

x-y+3z=3

Problem 2.

x-y+z=14

3x+2y+z=19

-2x+y-z=-21

I just want to know the steps on how to solve it one by one and I could solve the problem but as of now I am clueless on how to solve it. If you guys could help me out I would really appreciate it. Thank you in advance.

Re: solve system of equations using row operations on augmented matrix

[1 1 -1 : 5]

[1 2 -3 : 9]

[1 -1 3 : 3]

The left side of the : is the coefficients of x,y,z in our system and the numbers on the right side are our values. We need to be this is row echloen form.

First replace row 2 by (-row 2 + row 1). Then

[1 1 -1 : 5]

[0 -1 2 : -4]

[1 -1 3 : 3]

Now, replace row 3 by (-row 3 + row 1). Then

[1 1 -1 : 5]

[0 -1 2 : -4]

[0 2 -4 : -2]

Now multiply row 2 by -1. Then

[1 1 -1 : 5]

[0 1 -2 : 4]

[0 2 -4 : -2]

Now, replace row 3 by (-1/2 row 3 + row 2). Then

[1 1 -1 : 5]

[0 1 -2 : 4]

[0 0 0 : 5]

This third row implies that 0x + 0y + 0z = 5 i.e. 0 = 5 which is impossible. No solution!

Re: solve system of equations using row operations on augmented matrix

Hello, irv1234!

Here's the second one.

. . .