## Linear Algebra and Its Applications (5th Edition)

$\begin{bmatrix} \blacksquare&*&*\\ 0&\blacksquare&*\\ 0&0&\blacksquare \end{bmatrix}$
Recall that $\blacksquare$ represents a pivot and $*$ represents any numerical entry, including $0$. A matrix has linearly independent columns if and only if it contains a pivot in every column, leaving no free variables in the corresponding homogeneous matrix equation. By the rules defining an echelon matrix, the result must have the form above.