Solve the given matrix equation for α, or explain why no solution exists:

The given equation

gives a system of six equations in α:

3α − 4 = 2

α − 1 = 1

2α − 3 = 1

−2 = −2

α = 2

4α − 1 = 6.

Solving each of these equations, we see that the first three and the fifth all lead to the solution α = 2, the fourth equation is true no matter what the value of α, but the last equation is only solved by α = 7/4. Thus, the system has no solution, and the original matrix equation also has no solution.