Question
Prove that $\operatorname{ker} A \subseteq \operatorname{ker} A^2$. More generally, prove $\operatorname{ker} A \subseteq \operatorname{ker} B A$ for every compatible matrix $B$.
Step 1
The kernel of a matrix \( A \), denoted as \( \operatorname{ker} A \), is the set of all vectors \( \mathbf{x} \) such that \( A\mathbf{x} = \mathbf{0} \), where \( \mathbf{0} \) is the zero vector. Show more…
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