Next: 4 Equations in Matrix
Up: 4 Inverse of a
Previous: 4 Inverse of a
Index
In order to invert a matrix, the following four steps can be used:
ex2html_comment_mark>103
0.bean2
 <
 Find the determinant
 <
 Set up the matrix of cofactors
 <
 Transpose the matrix of cofactors
 <
 Divide by the determinant
For example, the matrix
can be inverted by:
ex2html_comment_mark>104
0.bean3
 <

 <

 <

 <

To verify this, we can multiply AA to obtain the identity
matrix:
The result that
may be used to solve the pair
of simultaneous equations:
which may be written
i.e.,
premultiplying both sides by the inverse of , we have
which may be verified by substitution.
For a larger matrix it is more tedious to compute the inverse. Let us
consider the matrix
ex2html_comment_mark>105
0.bean3
 <
 The determinant is
 <
 The matrix of cofactors is:
 <
 The transpose is
 <
 Dividing by the determinant, we have
which may be verified by multiplication with A to obtain the identity
matrix.
Next: 4 Equations in Matrix
Up: 4 Inverse of a
Previous: 4 Inverse of a
Index
Jeff Lessem
20020321