# An Analogy with Regular Algebra

As we saw in the video, solving matrix-vector equations is as simple as multiplying both sides of the equation by $$A$$'s inverse, $$A^{-1}$$, should it exist. The analogy with solving linear equations like $$5x = 7$$ is a good one.

If $$A^{-1}$$ doesn't exist, this does not work. The equivalent analogy for linear equations would be a situation in which the coefficient in front of the $$x$$ were $$0$$, which is the only real number that does not have an inverse. Which of the following does NOT analogize in this situation?