SOLUTION: Find the inverse for the given matrix If A= [ -4 0 0 0] [-1 2 0 0 ] [-4 4 4 0 ] [-1 -9 -1 1] Then A^-1=

 


Augment it with the identity matrix:



The idea is to make the left side become the
identity matrix, and then the right side
will become the inverse:

Multiply Row 2 by -4:



Add Row 1 to Row 2



Multiply Row 3 by -1



Add Row 1 to Row 3:



Multiply Row 4 by -4



Add Row 1 to Row 4




Multiply  Row 3 by -2



Add Row 2 to Row 3:



Multiply Row 2 by 9, and multiply Row 4 by 2



Add Row 2 to Row 4:



Multiply Row 3 by -1:



Add Row 3 to Row 4



Now divide the Row 1 through by -4,
divide Row 2 through by -72,
divide Row 3 through by -8
divide Row 4 through by -8



Now we have the identity on the left, so the inverse is 
the 4x4 matrix on the right, that is:



Edwin