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Remark. This is a helpful theorem from the standpoint of theory. To find the number of nonpivot columns of $A$, let

1. $p=\mathrm{\#}$ of pivot columns of $U$, where $U=\text{RREF}(A)$ is the 17.3 Reduced Row Echelon Form of $A$.
2. $p$ is the number of linearly independent columns of $A$.
3. The number of nonpivot columns of $A$ equals $d=(n-p)$.
4. The number of nonpivot columns of $A$ is the number of linearly dependent columns of $A$.
5. $d$ is the number of linearly independent solutions to the homogenous solution $A\cdot \overrightarrow{x}=\overrightarrow{0}$.

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