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(C) Matrices $P$ and $Y$ are of the orders $p 	imes k$ and $3 	imes k$ respectively.For the product $PY$ to be defined,the number of columns in $P$

Vedclass · Accepted Answer

$k=3, p=n$

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(C) Matrices $P$ and $Y$ are of the orders $p 	imes k$ and $3 	imes k$ respectively.For the product $PY$ to be defined,the number of columns in $P$ must equal the number of rows in $Y$. Thus,$k=3$.The resulting matrix $PY$ has the order $p 	imes k$.Matrices $W$ and $Y$ are of the orders $n 	imes 3$ and $3 	imes k$ respectively.The product $WY$ is defined because the number of columns in $W$ $(3)$ equals the number of rows in $Y$ $(3)$.The resulting matrix $WY$ has the order $n 	imes k$.For the sum $PY + WY$ to be defined,the matrices $PY$ and $WY$ must have the same order.Since $PY$ is $p 	imes k$ and $WY$ is $n 	imes k$,we must have $p=n$.Therefore,the restrictions are $k=3$ and $p=n$.

Assume $X, Y, Z, W$ and $P$ are the matrices of order $2 \times n, 3 \times k, 2 \times p, n \times 3$ and $p \times k$ respectively. The restriction on $n, k$ and $p$ so that $PY + WY$ will be defined are:

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