If A = [1 ,2 ,3],B = [ l 2 3 4 ] and C = [ * 20 c 1&5 0&2 ], then… - Vidyadip

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.

$BA$

b
(b) $BA = {\left[ \begin{array}{l}2\\3\\4\end{array} \right]_{3 \times 1}}\,{[1\,\,2\,\,3]_{1 \times 3}}$ $ = {\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.

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