Question

How do you solve using gaussian elimination or gauss-jordan elimination, `x+y-5z=-13`, `3x-3y+4z=11`, `x+3y-2z=-11`?

Answer 1

`x=-1, y=-2, z=2`

Explanation:

Initial Augmented Matrix:
#( (1, 1, -5, -13), ( 3, -3, 4, 11), ( 1, 3, -2, -11) )#

Using row 1 as pivot row and column 1 as pivot column
Non-pivot rows reduced for pivot column
#( ( 1, 1, -5, -13), ( 0, -6, 19, 50), ( 0, 2, 3, 2) )#

Using row 2 as pivot row
pivot row reduced:
#( ( 1, 1, -5, -13), ( 0, 1, -3.17, -8.33), ( 0, 2, 3, 2) )#

Non-pivot rows reduced for pivot column
#( ( 1, 0, -1.83, -4.67), ( 0, 1, -3.17, -8.33), ( 0, 0, 9.33, 18.67) )#

Using row 3 as pivot row
pivot row reduced:
#( ( 1, 0, -1.83, -4.67), ( 0, 1, -3.17, -8.33), ( 0, 0, 1, 2) )#

Non-pivot rows reduced for pivot column
#( ( 1, 0, 0, -1), ( 0, 1, 0, -2), ( 0, 0, 1, 2) )#