Answer
See explanation
Work Step by Step
Assumption
Put $T: \mathbb{R}^{n} \mapsto \mathbb{R}^{m}$ bet a linear transformation with
$A$ its standard matrix
Given
Statement:
$T$ is one-to-one if and only if $A$ has - - pivot columns.
Goal
a.) Complete the statement.
b.) Explain why the statement is true.
Solve (a.)
$T$ is one-to-one if and only if $A$ has $n$ pivot columns
The statement is true since if $A$ has $n$ pivot columns, so the columns of $A$ will always be linearly independent of each other.
