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

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}1&2&{ - 1}\\3&0&{\,\,2}\\4&5&{\,\,0}\end{array}} \right]$, $B = \left[ {\begin{array}{*{20}{c}}1&0&0\\2&1&0\\0&1&3\end{array}} \right],$then $AB$ is

✓
$\left[ {\begin{array}{*{20}{c}}5&1&{ - 3}\\3&2&6\\{14}&5&0\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}{11}&4&3\\1&2&3\\0&3&3\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}1&8&4\\2&9&6\\0&2&0\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}0&1&2\\5&4&3\\1&8&2\end{array}} \right]$

✓

Answer

Correct option: A.

$\left[ {\begin{array}{*{20}{c}}5&1&{ - 3}\\3&2&6\\{14}&5&0\end{array}} \right]$

a
(a) $A = \left[ {\begin{array}{*{20}{c}}1&2&{ - 1}\\3&0&2\\4&5&0\end{array}} \right]$, $B = \left[ {\begin{array}{*{20}{c}}1&0&0\\2&1&0\\0&1&3\end{array}} \right]$

$AB = \left[ {\begin{array}{*{20}{c}}{1 \times 1 + 2 \times 2 + ( - 1)(0)}\\{3 \times 1 + 0 \times 2 + 2 \times 0}\\{4 \times 1 + 5 \times 2 + 0 \times 0}\end{array}} \right.$

$\left. {\begin{array}{*{20}{c}}{1 \times 0 + 2 \times 1 + ( - 1)\,(1)}\\{3 \times 0 + 0 \times 1 + 2 \times 1}\\{4 \times 0 + 5 \times 1 + 0 \times 1}\end{array}\begin{array}{*{20}{c}}{\,\,\,\,1 \times 0 + 2 \times 0 + ( - 1)\,(3)}\\{3 \times 0 + 0 \times 0 + 2 \times 3}\\{4 \times 0 + 5 \times 0 + 0 \times 3}\end{array}} \right]$

$\therefore \,\,AB = \left[ {\begin{array}{*{20}{c}}5&1&{ - 3}\\3&2&6\\{14}&5&0\end{array}} \right]$.

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