If A is a 3 times 4 matrix and B is a matrix | vedclass

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(A) Given that $A$ is a $3 	imes 4$ matrix. Then,the transpose matrix $A^{\prime}$ is a $4 	imes 3$ matrix. For the product $A^{\prime}B$ to be defi

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$3 	imes 4$

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(A) Given that $A$ is a $3 	imes 4$ matrix. Then,the transpose matrix $A^{\prime}$ is a $4 	imes 3$ matrix. For the product $A^{\prime}B$ to be defined,the number of columns in $A^{\prime}$ must equal the number of rows in $B$. Since $A^{\prime}$ is $4 	imes 3$,$B$ must have $3$ rows. For the product $BA^{\prime}$ to be defined,the number of columns in $B$ must equal the number of rows in $A^{\prime}$. Since $A^{\prime}$ has $4$ rows,$B$ must have $4$ columns. Therefore,$B$ must be a $3 	imes 4$ matrix.

If $A$ is a $3 \times 4$ matrix and $B$ is a matrix such that $A^{\prime}B$ and $BA^{\prime}$ are both defined,then $B$ is of the type:

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