Example 1

Find the LU decomposition of the matrix

Solution

The matrix is the same as found at the end of the forward elimination of Naïve Gauss elimination method, that is

To find and , what multiplier was used to make the and elements zero in the first step of forward elimination of Naïve Gauss Elimination Method

It was

= 2.56

= 5.76

To find , what multiplier was used to make element zero. Remember element was made zero in the second step of forward elimination. The matrix at the beginning of the second step of forward elimination was

So

= 3.5

Hence

Confirm

.