MCQ
If $A = [1\,2\,3],B = \left[ \begin{array}{l}2\\3\\4\end{array} \right]$ and $C = \left[ {\begin{array}{*{20}{c}}1&5\\0&2\end{array}} \right],$ then which of the following is defined
- A$AC$
- ✓$BA$
- C$(AB)\,{\rm{. }}C$
- D$(AC)\,.\,B$
✓
Answer
Correct option: B.
$BA$
$BA = {\left[ \begin{array}{l}2\\3\\4\end{array} \right]_{3 \times 1}}\,{[1\,\,2\,\,3]_{1 \times 3}}$
$ = {\left[ {\begin{array}{*{20}{c}}2&4&6\\3&6&9\\4&8&{12}\end{array}} \right]_{3 \times 3}}$
$AB = {[1\,2\,3]_{1 \times 3}}{\left[ \begin{array}{l}2\\3\\4\end{array} \right]_{3 \times 1}} ={[20]_{1 \times 1}}$.
So, $AB$ and $BA$ are defined.
$ = {\left[ {\begin{array}{*{20}{c}}2&4&6\\3&6&9\\4&8&{12}\end{array}} \right]_{3 \times 3}}$
$AB = {[1\,2\,3]_{1 \times 3}}{\left[ \begin{array}{l}2\\3\\4\end{array} \right]_{3 \times 1}} ={[20]_{1 \times 1}}$.
So, $AB$ and $BA$ are defined.
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| $R$ The function $f_3$ is | $3$ differentiable at $x=0$ and its derivative is $\text{NOT}$ continuous at $x =0$ |
| $S$ The function $f _4$ is | $4$ differentiable at $x =0$ and its derivative is continuous at $x =0$ |