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