Write the augmented matrix for the given system of equations.



A augmented matrix has no solution if a row 
has all 0's except for a non-zero element, say 1,
for the rightmost element.  For it would
represent the equation 0x+0y+0z+0w=1.

We try to get a row with all 0's except for
a non-zero element for a rightmost element.
Multiply row 1 by 3 and add to row 2:





Multiply row 1 by -2 and add to row 3:





Multiply row 2 by 3 and add to row 3:





The bottom row will represent an equation with
no solution if:



If p=1, the first two equations will be true.
The inequality will hold if 

Answer: , 

Edwin