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Let \(A\) and \(B\) be \(n \times n\) matrices.

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Let \(A\) and \(B\) be \(n \times n\) matrices.
a) Show that the \(\operatorname{rank}(A B) \leq \operatorname{rank}(A)\). Give an example where strict inequality can occur.
b) Show that \(\operatorname{dim}(\operatorname{ker} A B) \geq \operatorname{dim}(\operatorname{ker} A)\). Give an example where strict inequality can occur.
in Mathematics by ♦ Platinum (164,920 points) | 119 views

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MathsGee Android Q&A

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