** Gauss-Jordan Method Solving a Linear System**

**1. **Write each equation so that variable terms are in the same order on the left

side of the equals sign and constants are on the right.

**2. **Write the augmented matrix that corresponds to the system.

**3. **Use row operations to transform the first column so that all elements

except the element in the first row are zero.

**4. **Use row operations to transform the second column so that all elements

except the element in the second row are zero.

**5. **Use row operations to transform the third column so that all elements

except the element in the third row are zero.

**6. **Continue in this way, when possible, until the last row is written in the

Form

[0 0 0 ……0 j │k],

where *j *and *k *are constants with j ≠ 0. When this is not possible, continue

until every row has more zeros on the left than the previous row (except

possibly for any rows of all zero at the bottom of the matrix), and the first

nonzero entry in each row is the only nonzero entry in its column.

**7. **Multiply each row by the reciprocal of the nonzero element in that row.