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Part 3 - How do I find the inverse of a square matrix using LU Decomposition?

Posted by BMFRGuru at 7:52 PM

Example 3

Use LU decomposition to find the inverse of

Knowing that

We can solve for the first column of [B]=by solving for

First solve

, that is

to give

Forward substitution starting from the first equation gives

Hence

Now solve

that is

Backward substitution starting from the third equation gives

=

= -0.9524

= 0.04762

Hence the first column of the inverse of [A] is

Similarly by solving

and solving

gives

Hence

Can you confirm the following for the above example? =

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