A = [3x3] Matrix =

-1 3 -1

2 -2 3

-1 1 2

How Do We Get (A)^(-1) (The inverse of A)?

I would show an attempt at the solution, however, I am clueless about this.

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- Mar 22nd 2011, 11:10 AMAlphaRockHow To Get The Inverse In A 3x 3 Matrix?
A = [3x3] Matrix =

-1 3 -1

2 -2 3

-1 1 2

How Do We Get (A)^(-1) (The inverse of A)?

I would show an attempt at the solution, however, I am clueless about this. - Mar 22nd 2011, 11:19 AMAckbeet
Try this: append the matrix $\displaystyle I$ to $\displaystyle A$ thus:

$\displaystyle [A|I]=\left[

\begin{array}{rrr|rrr}

-1 &3 &-1 &1 &0 &0\\

2 &-2 &3 &0 &1 &0\\

-1 &1 &2 &0 &0 &1

\end{array}\right].$

Now perform on this entire matrix the row operations necessary to get to reduced row echelon form; that is, you take $\displaystyle A\to I.$ Then you'll have

$\displaystyle [A|I]\to[I|A^{-1}].$

All of this assumes, of course, that $\displaystyle A$ is invertible.

Make sense? - Mar 22nd 2011, 12:34 PMpickslides
If Ackbeet's method is a bit tricky then try using some software like MATLAB to solve it for you.

- Mar 22nd 2011, 12:40 PMdwsmith
- Mar 22nd 2011, 12:48 PMpickslides
- Mar 22nd 2011, 12:50 PMAckbeet
- Mar 22nd 2011, 12:51 PMdwsmith
- Mar 22nd 2011, 01:00 PMAckbeet
- Mar 23rd 2011, 04:48 AMmr fantastic