Let A be an n x n matrix. How do you show that the rows of A are linearly independent if and only if the columns of A span $R^{n}$?
Let A be an n x n matrix. How do you show that the rows of A are linearly independent if and only if the columns of A span $R^{n}$?
the rows of $A$ are linearly independent iff the columns of $A^T$ are linearly independent iff $A^T$ is invertible iff $A$ is invertible iff the columns of $A$ are linearly independent iff the columns of $A$ span $\mathbb{R}^n.$