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x_{1}+ 3x_{2}- x_{3}= b_{1}

x_{1}- x_{2}+ 3x_{3}= b_{1}

-2x_{1}- 5x_{2}- x_{3}= b_{1}

So using an augmented matrix I get this

[1 3 -1 | 1]

[1 -1 3 | 1]

[-2 -5 1 | 1]

[1 3 -1 | 1]

[0 -4 4 | 0] R2 - R1 = R2

[0 1 -1 | 3] R3 + 2R1 = R3

[1 3 -1 | 1]

[0 1 -1 | 3] Swap R2 with R3

[0 -4 4 | 0]

[1 0 2 | -8] R1 - 3R2 = R1

[0 1 -1 | 3]

[0 0 0 | 12] R3 + 4R2 = R3

Now my problem is the third row

I don't know how to use this to answer this part of the question

"Use part b) to write an equation that expresses conditions on b1, b2 and b3 so that the system

will be consistent."

Have I reduced it correctly? Is there another way to reduce it?

If not how do I answer that part of the question?

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# System of Linear Equations to Reduced Echelon Form

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