Note that the system of linear equations does not have a solution only if the determinant of is 0, the determinant of this matrix is which is 0 at (using quadratic formula) A = -5, A = 2

so to see plug in A = -5, and to verify if the system is inconsistent, first note that By simple examination i see that so the last column vector is linearly dependent, so we can throw it out.

Now is aking to solving

so by observation we note that a solution of this system must have x = -3, which constraints y = so our soln, if we have one is but

which does not equal Thus for A = -5, this system is inconsistent (has no solutions).

Now for A = 2, using the above analysis, it has an infinitely many soln.

So only for A = -5, the system of lin eqn is inconsistent.