Chapter 3: Matrices

Ans: The correct option is Option(A)

Matrices $P$ and $Y$ are of the orders $p \times k$ and $3 \times k$ respectively.

Therefore, matrix PY will be defined if $\mathrm{k}=3$.

Consequently, $P Y$ will be of the order $p \times k$.

Matrices $\mathrm{W}$ and $\mathrm{Y}$ are of the orders $\mathrm{n} \times 3$ and $3 \times \mathrm{k}$ respectively.

Since the number of columns in $\mathrm{W}$ is equal to the number of rows in $\mathrm{Y}$, matrix $\mathrm{WY}$ is well-defined and is of the order $\mathrm{n} \times \mathrm{k}$.

Matrices PY and WY can be added only when their orders are the same.

However, PY is of the order $\mathrm{p} \times \mathrm{k}$ and $\mathrm{WY}$ is of the order $\mathrm{n} \times \mathrm{k}$. Therefore. we must have $\mathrm{p}=\mathrm{n}$.

Thus, $\mathrm{k}=3$ and $\mathrm{p}=\mathrm{n}$, are the restrictions on $\mathrm{n}, \mathrm{k}$ and $\mathrm{p}$ so that $\mathrm{PY}+\mathrm{WY}$ will be defined.

Ans: The correct answer is B.

Matrix $X$ is of the order $2 \times n$.

Therefore, matrix $7 \mathrm{X}$ is also of the same order.

Matrix $Z$ is of the order $2 \times p$ or $2 \times n$ (Because $n=p$ )

Therefore, matrix $5 \mathrm{Z}$ is also of the same order.

Now, both the matrices $7 \mathrm{X}$ and $5 \mathrm{Z}$ are of the order $2 \times \mathrm{n}$.

Thus, matrix $7 \mathrm{X}-5 \mathrm{Z}$ is well-defined and is of the order $2 \times \mathrm{n}$.