(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the following system of equations using Gaussian Elimination:

-2a+5c=1

a+2b-c=2

3a-2b=3

2. Relevant equations

N/A

3. The attempt at a solution

Augmented matrix

(-2 0 5 | 1) R2 → R2 +R1/2

(1 2 -1 | 2) R3 → R3 - 3R2

(3 -2 0 | 3)

(-2 0 5 | 1) Swap R2 and R3

(0 2 3/2 | 5/2)

(0 -8 0 | -3)

(-2 0 5 | 1) R2 → -R2/4

(0 -8 0 | -3)

(0 2 3/2 | 5/2)

(-2 0 5 | 1) R3 → R3-R2

(0 2 0 | 3/4)

(0 2 3/2 | 5/2)

(-2 0 5 | 1) R3 → R3*10/3

(0 2 0 | 3/4)

(0 2 3/2 | 5/2)

(-2 0 5 | 1) R1 → R1-R3

(0 2 0 | 3/4)

(0 0 5 | 7/12)

(-2 0 0 | 5/12)

(0 2 0 | 3/4)

(0 0 5 | 7/12)

therefore a=-5/24, b=3/8 and c=7/60

The problem is a and c satisfy the equation but b does not, not sure what i've done wrong especially since a and c both work. Any help?

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# Homework Help: Solving via Gaussian Elimination

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