Finding inverse of a matrix (A^-1)

May 2010
7
0
find the inverse of

1 2 -3
3 2 -1
2 1 3

if there is
 
Last edited:
May 2010
13
3
how to find the inverse

The inverse can be found by setting this matrix equal to the identity matrix and row reducing so that the identity matrix is on the other side of equal sign (the inverse matrix will be where the identity matrix is originally).
So
1 2 -3 | 1 0 0
3 2 -1 | 0 1 0
2 1 3 | 0 0 1

Does that help?
 
Dec 2009
872
381
1111
find the inverse of

1 2 -3
3 2 -1
2 1 3

if there is
Dear swiftshift,

\(\displaystyle \left(\begin{array}{ccc}1&2&-3\\3&2&-1\\2&1&3\end{array}\right)\times\left(\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right)=\left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right)\)

By matrix multiplication you could obtain nine equations and solve for the unknowns.
 
Last edited:
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May 2010
7
0
The inverse can be found by setting this matrix equal to the identity matrix and row reducing so that the identity matrix is on the other side of equal sign (the inverse matrix will be where the identity matrix is originally).
So
1 2 -3 | 1 0 0
3 2 -1 | 0 1 0
2 1 3 | 0 0 1

Does that help?
thanks mate
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Dear swiftshift,

\(\displaystyle \left(\begin{array}{ccc}1&2&-3\\3&2&-1\\2&1&3\end{array}\right)\times\left(\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right)=\left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right)\)

By matrix multiplication you could obtain six equations and solve for the unknowns.
Actually, you get nine equations for the nine unknowns. Probably not the best way to find an inverse!
 
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