How do you find the determinant

One perfectly good method would be to try to solve that system of equations by the usual "elimination" methods (I would be inclined to subtract one equation from the other) and see what values of a make it impossible to solve the equationl (For example, you can't divide by 0.)

By the way, the question (which I notice is NOT part of the copied statement) is not well phrased. The is NO value of a "for which there will be no solution". There is a value of a for which either there is no solution or there are an infinite number of solutions, depending on b.

 

by making a 1 you are making the matrix cingular because the row vectors are now linearlly dependent. I think the method you're using should work also... You would get
a-1 = 0...

 

Two straight lines will always intersect except if what about the lines are the same?