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

- anonymous

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

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- anonymous

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

- Hero

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

- anonymous

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

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## More answers

- Hero

How far have you gotten with reducing the matrix?

- anonymous

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

- Hero

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

- anonymous

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

- Hero

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

- anonymous

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

- Hero

May I suggest a different approach?

- anonymous

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.

- anonymous

Of course!

- Hero

What if, starting with the original matrix, you performed the following operations to start with:
R2 + R3, then 2R1 + R2

- anonymous

Just row 2 + row 3? not multiplying anything?

- Hero

Yes, actually do
R2 + R3, then -2R1 + R2

- anonymous

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

- anonymous

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

- anonymous

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

- Hero

You should double check your work for those 2 operations.

- anonymous

okay, what's wrong with it?

- anonymous

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

- Hero

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

- anonymous

Ah. Would it be a 4?

- Hero

Yes

- anonymous

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

- Hero

You're jumping too far ahead.

- Hero

Please post just the first two operations.

- anonymous

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

- Hero

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.

- anonymous

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

- Hero

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.

- anonymous

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

- Hero

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

- anonymous

Okay, that makes sense.
Thank you!

- Hero

You're welcome. Great work on your problem.

- anonymous

Thank you!

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