How to solve this homogenous linear system corresponding to the coefficient matric provided using the Gauss- Jordan Elimination Method?

Question

2 2 -1 0 1

-1 -1 2 -3 1

1 1 -2 0 -1

0 0 1 1 1

Answer 1

The Gauss-Jordon elimination method employs the following rules:

1. Swap the positions of two of the rows
2. Multiply one of the rows by a nonzero scalar.
3. Add or subtract the scalar multiple of one row to another row.

You repeat these steps until the matrix is in the reduced-row echelon form. That means you have 1's on the diagonal and all zeroes in the lower left part of the matrix.

1 a b c d

0 1 e f g

0 0 1 h i

0 0 0 1 k

Then you can back substitute to solve the system of equations, starting with the bottom row. For example, if the variables in your case are x, y, z and w.

w = k

z + hw = i

y + ez + fw = g

x + ay +bz +c w = d