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

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

Mathematics
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I know that we are to end up with a matrices in the form of 1 ? ? ? 0 1 ? ? 0 0 1 ?
@LadyInkblot have you converted the system to a matrix yet?
Yes. It starts out as a matrix of 1 -5 4 -3 2 -7 3 -2 -2 1 7 -1

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How far have you gotten with reducing the matrix?
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
Looks like you attempted to perform a couple of row operations. Do you remember which row operations you performed?
I preformed (I believe) 2R1 + R3 and -2R1 - R2
I can double check that for you. In the mean time, do you know how you plan to continue reducing the matrix from here?
I do not know how to proceed, which is why I came here for help ^_^;
May I suggest a different approach?
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.
Of course!
What if, starting with the original matrix, you performed the following operations to start with: R2 + R3, then 2R1 + R2
Just row 2 + row 3? not multiplying anything?
Yes, actually do R2 + R3, then -2R1 + R2
okay. I'll get back to you in a minute then with my answer...
Okay, so I got 1 -5 4 -3 0 3 -5 0 0 6 -4 -4
But then I'll still have to get rid of the 6 in the third row... so what about 2R2 + r3?
You should double check your work for those 2 operations.
okay, what's wrong with it?
Okay, I tried again and got something different 1 -5 4 -3 0 3 -5 -8 0 -6 10 -3
The 1st and 3rd row are correct. The second row has a mistake with the -8
Ah. Would it be a 4?
Yes
1 -5 4 -3 0 3 -5 4 0 0 0 5
You're jumping too far ahead.
Please post just the first two operations.
1 -5 4 -3 0 3 -5 4 0 -6 10 -3
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.
Yes. What does that mean, an invalid row. 1 -5 4 -3 0 3 -5 4 0 0 0 5
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.
Okay. So what does that mean for the answer to the problem then. Just that the solution is invalid?
It means the system cannot be solved and therefore has no solution.
Okay, that makes sense. Thank you!
You're welcome. Great work on your problem.
Thank you!

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