Question

Let a matrix $A=[a_{ij}{]}_{m\times n}$ is defined as $a_{ij}=mn$ and $m^2-1\ge 0,n^2-9\le 0.$ Then matrix $A$ can be a

• A. Null matrix
• B. Scalar matrix
• C. Row matrix
• D. Column matrix

Answer 1

Answer: (C), (D)

Column matrix

Given : $a_{ij}=mn\cdots \left(i\right)$
For matrix to be defined, $m\ge 1,n\ge 1$ and $m,n\in Z\cdots \left(ii\right)$

$m^2-1\ge 0$ and $n^2-9\le 0$
$\Rightarrow m\le -1$ or $m\ge 1$ and $-3\le n\le 3\cdots \left(iii\right)$
From $\left(ii\right)$ and $\left(iii\right)$, we get
$m\ge 1$ and $1\le n\le 3$
$\therefore a_{ij}=mn\ge 1$
As, no elements of $A=\left[a_{ij}\right]$ can be zero.
So matrix $A$ can not be a null matrix or scalar matrix.

For $m=1,n>1:$ Matrix $A$ has one row.
So $A$ can be a Row matrix.

For $m>1,n=1:$ Matrix $A$ has one column.
So $A$ can be column matrix.