Question

Let $A$ be an $m \times n$ matrix. What are the permissible sizes for the zero matrices appearing in the identities $A \mathrm{O}=\mathrm{O}$ and $\mathrm{O} A=\mathrm{O}$ ?

    Let $A$ be an $m \times n$ matrix. What are the permissible sizes for the zero matrices appearing in the identities $A \mathrm{O}=\mathrm{O}$ and $\mathrm{O} A=\mathrm{O}$ ?

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Peter J. Olver,… 2nd Edition

Chapter 1, Problem 17

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Step 1

Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. If $A$ is an $m \times n$ matrix, then for the product $A \mathrm{O}$ to be defined, $\mathrm{O}$ must have $n$ rows. Similarly, for Show more…

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Let $A$ be an $m \times n$ matrix. What are the permissible sizes for the zero matrices appearing in the identities $A \mathrm{O}=\mathrm{O}$ and $\mathrm{O} A=\mathrm{O}$ ?

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