Question

If $A=\left[\begin{array}{ll}3 & 5\end{array}\right]$ and $B=\left[\begin{array}{ll}7 & 3\end{array}\right]$, then the order of a non-zero matrix $C$ such that $A C$ and $B C$ are defined, is

• A. $1 \times n$
• B. $2 \times n$
• C. $1 \times 2$
• D. $3 \times 1$

Answer 1

Answer: (B)

The given matrices are $A=\left[\begin{array}{ll}3 & 5\end{array}\right]$ and $B=\left[\begin{array}{ll}7 & 3\end{array}\right]$
$\because A C$ is defined and $A$ has 2 columns.
$\therefore C$ has 2 rows.
Also, $B C$ is defined and $B$ has 2 columns.
$\therefore $ C has 2 rows.
Also, this matrix can have any numbers of columns, since $A C$ and $B C$ are defined.
$\therefore $ Order of $C=2 \times n, n \in N$