
Inverse Matrices Problem
Hi
The following question, can someone tell me if this is the right method of doing it.
If, and , find conditions on a, b and c so the system of equations represented by CX = D has an infinite number of solutions.
previous question asked to find det C =
det C = b +2a22
i made b=0 to find a which equals 11 therefore det C =0 and c=0 when i made the equation
P.S

You need to remember the following fact:
A matrix has an inverse, if and only if .
You are choosing and , such that , in which case the matrix is not invertible, so the expression " " does not make sense in this case.

so how would you suggest i approach this question.

I would do it in the "oldfashioned" way. To solve the equation for , you rowreduce the augmented matrix
For some values of , , and , the last row may end up looking like
in which case there are no solutions. On the other hand, the last row could also end up looking like
in which case you need to consider, if the last variable (the variable) can be a free variable, thus giving rise to an infinite number of solutions.