Question

How do you solve using gaussian elimination or gauss-jordan elimination, `x+y+z=3`, `2x+2y-z=3`, `x+y-z=1`?

Answer 1

This set of equations has no solution

Explanation:

Initial Augmented Matrix:
#[ ( 1.00, 1.00, 1.00, 3.00), ( 2.00, 2.00, -1.00, 3.00), ( 1.00, 1.00, -1.00, 1.00) ]#

Pivot Action `n`
pivot row = n; pivot column = n; pivot entry augmented matrix entry at (n,n)

1. convert pivot n row so pivot entry = 1
2. adjust non-pivot rows so entries in pivot column = 0

Pivot `color(black)(1)`
Pivot Row 1 reduced by dividing all entries by 1.00 so pivot entry = 1
#[ ( 1.00, 1.00, 1.00, 3.00), ( 2.00, 2.00, -1.00, 3.00), ( 1.00, 1.00, -1.00, 1.00) ]#

Non-pivot rows reduced for pivot column
by subtracting appropriate multiple of pivot row 1 from each non-pivot row

#[ ( 1.00, 1.00, 1.00, 3.00), ( 0.00, 0.00, -3.00, -3.00), ( 0.00, 0.00, -2.00, -2.00) ]#

Pivot `color(black)(2)`
Pivot row 2 has a 0-valued pivot entry; exchange attempted
No subsequent rows have a non-zero value in the pivot column

*************************************
Given equations allow for no solution
*************************************