Question

If $O(A) = 2 \times 3, O (B) = 3 \times 2$, and $O(C) = 3 \times 3$, which one of the following is not defined.

• A. $C(A+B')$
• B. $C(A+B')'$
• C. $BAC$
• D. $CB+A'$

Answer 1

Answer: (A)

Given that $O\left(A\right) = 2 \times3 , O\left(B\right) = 3\times 2 $ and $ O\left(C\right) = 3 \times3 $
$ \Rightarrow \, O\left(A'\right) = 3 \times2 , O\left(B'\right) = 2\times 3$
(a) $CB+A' $
Now order of CB = (order of C) (order of B)
= (order of C is $3 \times 3$) (order of B is $3 \times 2$)
= order of CB is $3 \times 2$
Since $O(A' ) = 3 \times 2$
$\therefore $ Matrix CB + A' can be determined.
(b) $O(BA) = 3 \times 3$
and $O(C) = 3 \times 3$
$\therefore $ Matrix BAC can be determined.
(c) $C(A + B')'$
$O(A + B') = 2 \times 3$
$\Rightarrow \; O(A + B')' = 3 \times 2$
and $O(C) = 3 \times 3$
$\therefore $ Matrix $C(A + B')'$ can be determined.
(d) $C(A + B')$
$O(A + B') = 2 \times 3$
and $O(C) = 3 \times 3$
$\therefore $ Matrix $C (A + B')$ cannot be determined