Question

Use Gauss-Jordan elimination to solve the following linear system:
5x-2y=-2
-x+4y=4

Answer 1

x = 0 y = 1.

Explanation:

Write it in matrix form ( r1 and r2 refer to row 1 and row 2):-

( 5 -2 | -2) r1

(-1 4 | 4) r2

4r2 + r1 --> r1 :

( 1 14 | 14)

(-1 4 | 4)

r2 + r1 ---> r2

( 1 14 | 14)

( 0 18 | 18)

r2 / 18:

( 1 14 | 14)

( 0 1 | 1) So y = 1.

r1 - 14r2 = r1

( 1 0 | 0) x = 0

( 0 1 | 1)