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solve by using gaussian elimination:

3x - y + z = 1

2x + 2y – 5z = 0

5x + y – 4z = 7

what i did:

step 1: new row 1 = old row 1 – row 2, I got:

x – 3y + 6z = 1

2x + 2y – 5z = 0

5x + y – 4z = 7

step 2: new row 2 = old row 2 – (2 * row1) and new row 3 = old row 3 – (5 * row 1), I got:

x – 3y + 6z = 1

0 + 8y – 17z = -2

0 + 16y – 34z = 2

step 3: new row 3 = old row 3 * (1/2) I got:

x – 3y + 6z = 1

0 + 8y – 17z = -2

0 + 8y – 16z = 1

step 4: new row 3 = old row 3 – row 2, I got:

x – 3y + 6z = 1

0 + 8y – 17z = -2

0 + 0 + z = 3

the Real Answer:

Gaussian elimination gives 0z = 6, ie, 0 = 6 which is clearly impossible.

NO solutions.

i obviously didn’t get that, and i would really appreciate it if someone could check whether i am going wrong somewhere or if my teacher is wrong

thanx

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# Homework Help: Gaussian Elimination

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