Answer
See solution
Work Step by Step
Put $T: \mathbb{R}^{n} \mapsto \mathbb{R}^{m}$ bet a linear transformation with $A$ its standard matrix
Given
Statement:
$T \operatorname{maps} \mathbb{R}^{n}$ onto $\mathbb{R}^{m}$ if and only if $A$ has pivot columns.
Goal
a.) Complete the statement.
b.) Clearing why the statement is true.
Solve (a.)
$T$ is onto if and only if $A$ has $m$ pivot columns.
Solve (b.)
The statement is true since if $A$ has $m$ pivot columns, then the columns of $A$ will always span $\mathbb{R}^{m}$
