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. $C(A+B^{\prime })$
• B. $C(A+B^{\prime }{)}^{\prime }$
• C. $BAC$
• D. $CB+A^{\prime }$

Answer 1

Answer: (A)

Given that $O\left(A\right)=2\times 3,O\left(B\right)=3\times 2$ and $O\left(C\right)=3\times 3$
$\Rightarrow O\left(A^{\prime }\right)=3\times 2,O\left(B^{\prime }\right)=2\times 3$
(a) $CB+A^{\prime }$
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 $O(A^{\prime })=3\times 2$
$\therefore$ 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) $C(A+B^{\prime }{)}^{\prime }$
$O(A+B^{\prime })=2\times 3$
$\Rightarrow O(A+B^{\prime }{)}^{\prime }=3\times 2$
and $O(C)=3\times 3$
$\therefore$ Matrix $C(A+B^{\prime }{)}^{\prime }$ can be determined.
(d) $C(A+B^{\prime })$
$O(A+B^{\prime })=2\times 3$
and $O(C)=3\times 3$
$\therefore$ Matrix $C(A+B^{\prime })$ cannot be determined