Question

Solve the system.
x1 - 5x2 + 4x3 = -3
2x1 - 7x2 + 3x3 = -2
-2x1 + x2 + 7x3 = -1

Answer 1

I know that we are to end up with a matrices in the form of
1 ? ? ?
0 1 ? ?
0 0 1 ?

Answer 2

@LadyInkblot have you converted the system to a matrix yet?

Answer 3

Yes.
It starts out as a matrix of
1 -5 4 -3
2 -7 3 -2
-2 1 7 -1

Answer 4

How far have you gotten with reducing the matrix?

Answer 5

I don't know if this is correct, but so far I have
1 -5 4 -3
0 3 -5 4
0 -10 15 -7

Answer 6

Looks like you attempted to perform a couple of row operations. Do you remember which row operations you performed?

Answer 7

I preformed (I believe) 2R1 + R3 and -2R1 - R2

Answer 8

I can double check that for you. In the mean time, do you know how you plan to continue reducing the matrix from here?

Answer 9

I do not know how to proceed, which is why I came here for help ^_^;

Answer 10

May I suggest a different approach?

Answer 11

I know that I need to get rid of the -10x2, but I'm not sure how to go about it, since I don't want anything to go back into my third row first column spot.

Answer 12

Of course!

Answer 13

What if, starting with the original matrix, you performed the following operations to start with:

R2 + R3, then 2R1 + R2

Answer 14

Just row 2 + row 3? not multiplying anything?

Answer 15

Yes, actually do

R2 + R3, then -2R1 + R2

Answer 16

okay. I'll get back to you in a minute then with my answer...

Answer 17

Okay, so I got
1 -5 4 -3
0 3 -5 0
0 6 -4 -4

Answer 18

But then I'll still have to get rid of the 6 in the third row... so what about 2R2 + r3?

Answer 19

You should double check your work for those 2 operations.

Answer 20

okay, what's wrong with it?

Answer 21

Okay, I tried again and got something different
1 -5 4 -3
0 3 -5 -8
0 -6 10 -3

Answer 22

The 1st and 3rd row are correct. The second row has a mistake with the -8

Answer 23

Ah. Would it be a 4?

Answer 24

Yes

Answer 25

1 -5 4 -3
0 3 -5 4
0 0 0 5

Answer 26

You're jumping too far ahead.

Answer 27

Please post just the first two operations.

Answer 28

1 -5 4 -3
0 3 -5 4
0 -6 10 -3

Answer 29

Okay, yes, and in the next step, you figure out that you have a row of the form 0 0 0 b which is an invalid row.

Answer 30

Yes. What does that mean, an invalid row.
1 -5 4 -3
0 3 -5 4
0 0 0 5

Answer 31

If you converted the last row back to an algebraic equation, you'd have the form 0x + 0y + 0z = 5 or just 0 = 5, but 0 = 5 is a false statement.

Answer 32

Okay. So what does that mean for the answer to the problem then. Just that the solution is invalid?

Answer 33

It means the system cannot be solved and therefore has no solution.

Answer 34

Okay, that makes sense.
Thank you!

Answer 35

You're welcome. Great work on your problem.

Answer 36

Thank you!