|
|
To find the inverse of the matrix Form the matrix Then perform row operations Answer:
where
To handle all three tasks perform row operations on the augmented matrix
The reduced row echelon form:
There are no solutions unless .
When , the transformed system of linear equations is:
and may be expressed as functions of and .
The variables corresponding to pivot columns may be expressed as functions of the other variables.
Every solution for the case when has the form as the parameters and range over all real values — a “plane” in the -dimensional space .
The set of for which has at least one solution — the image of — is the plane in given by the equation .
Every solution of has the form where is given by the formula above.
|