Question
Consider an $m \times n$ matrix $A$ with $\operatorname{ker}(A)=\{\overrightarrow{0}\} .$ Show that there exists an $n \times m$ matrix $B$ such that $B A=I_{n}$ Hint: $A^{T} A$ is invertible.
Step 1
This implies that the columns of $A$ are linearly independent. Show more…
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