Solve Ax = b when the dimension of b does not equal the dimension of A

Question

I am having trouble solving part b of this problem. I was able to solve part a, however, when I try to solve Ax = b and Ay =c I do not see how I can set up an augmented matrix and row reduce. The dimension of b and c are 4 but the dimension of the vectors in A are 3.

Does anybody know how to solve this?

Should I add a zero vector as the last row of A?

Answer 1

There must be a typo.

$A \in \mathbb{R}^{3 \times 3}$, $x \in \mathbb{R}^{3 \times 1}$, hence $Ax \in \mathbb{R}^{3 \times 1}$ and it cannot be equal to a vector of length $4$.