Hello everyone. I've been trying to come up with an answer to this question for a while now, however, I haven't had much luck.

My solution (first by reducing the matrix with elementary matrix operations):Find conditions on a, b, c, and d such that and has no solution.

I know that a system will be inconsistent if a row (in this case) takes the form of this vector:

Therefore, for the system to be inconsistent, it looks like , , or both should have to be zero. However, if , the first row becomes the zero vector. If , I get the zero vector in the second row. If I set both and equal to zero, I end up with an answer that doesn't quite make sense to me (because of the indeterminate 0/0 terms):

Now, if , the condition will be met, but I don't know how to reconcile the indeterminacy generated by the 0/0 quotients. Help would be greatly appreciated!