# How to determine fewest matrix rows that have entries for all columns?

My apologies for the poor title and description, it's been a long time since I had linear algebra (or any formal math class).

Given the following example matrix:

\begin{matrix} & W & X & Y & Z\end{matrix}

$$\begin{matrix}A\\B\\C\\D\\E\\F\\G\\H\end{matrix}\begin{bmatrix}1 & 1 & 0 & 1\\0 & 0 & 0 & 1\\0 & 0 & 1 & 0\\1 & 1 & 1 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 1 & 0\\0 & 1 & 0 & 1\end{bmatrix}$$

How would I determine the fewest number of rows (A-H) that select all of the columns (W-Z).

For example, in the matrix above, row A fulfills columns W, X, and Z and then row C, D, or G can then fulfill the remaining Y column.

Another example would be row D which fulfills columns W, X, and Y. We could then fulfill column Z with either row A, B, or H.

Again, please forgive me for the poor description and lack of appropriate terminology and language. Please let me know if I'm missing any information or need to clarify anything.