Page 70 - A Course in Linear Algebra with Applications

54 Chapter Two: Systems of Linear Equations

x
The procedure for computing A starts with the parti-
tioned matrix

[A | In]

and then puts it in reduced row echelon form. If A is invertible,
the reduced row echelon form will be

1
[In I A- ],

as the discussion just given shows. On the other hand, if the
procedure is applied to a matrix that is not invertible, it will
be impossible to reach a reduced row echelon form of the above
type, that is, one with I n on the left. Thus the procedure will
also detect non-invertibility of a matrix.

Example 2.3.5
Find the inverse of the matrix

A =

Put the matrix [A | J3] in reduced row echelon form, using
elementary row operations as described above:

1/2 0 0'
1/2 1 0
0 0 1