Question

How do you solve using gaussian elimination or gauss-jordan elimination, `x+y+z=7`, `x-y+2z=7`, `2x+3z=14`?

Answer 1

Please see the explanation for how you do it.

Explanation:

Make an augmented matrix of the coefficients of the 3 equations:

#[ (1,1,1,|,7), (1,-1,2,|,7), (2,0,3,|,14) ]#

Subtract row 1 from row 2:

#[ (1,1,1,|,7), (0,-2,3,|,0), (2,0,3,|,14) ]#

Multiply row 1 by -2 and add to row 3:

#[ (1,1,1,|,7), (0,-2,3,|,0), (0,-2,1,|,0) ]#

Subtract row 2 from row 3:

#[ (1,1,1,|,7), (0,-2,3,|,0), (0,0,-2,|,0) ]#

Divide row 3 by -2:

#[ (1,1,1,|,7), (0,-2,3,|,0), (0,0,1,|,0) ]#

Multiply row 3 by - 3 and add to row 2:

#[ (1,1,1,|,7), (0,-2,0,|,0), (0,0,1,|,0) ]#

Divide row 2 by -2:

#[ (1,1,1,|,7), (0,1,0,|,0), (0,0,1,|,0) ]#

Subtract row 3 from row 1:

#[ (1,1,0,|,7), (0,1,0,|,0), (0,0,1,|,0) ]#

Subtract row 2 from row 1:

#[ (1,0,0,|,7), (0,1,0,|,0), (0,0,1,|,0) ]#

`x = 7, y = 0, z = 0`

Check:

7 + 0 + 0 = 7
7 - 0 + 2(0) = 7
2(7) + 3(0) = 14

This checks