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

MCQ

If $P = \left[ {\begin{array}{*{20}{c}}1&2&3\\2&3&4\\3&4&5\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{ - 1}&{ - 2}\\{ - 2}&0\\0&{ - 4}\end{array}} \right]$$\left[ {\begin{array}{*{20}{c}}{ - 4}&{ - 5}&{ - 6}\\0&0&1\end{array}} \right]$ then ${P_{22}} = $

✓
$40$
B
$-40$
C
$-20$
D
$20$

✓

Answer

Correct option: A.

$40$

a
(a) $P = {\left[ {\begin{array}{*{20}{c}}1&2&3\\2&3&4\\3&4&5\end{array}} \right]_{3 \times 3}}{\left[ {\begin{array}{*{20}{c}}{ - 1}&{ - 2}\\{ - 2}&0\\0&{ - 4}\end{array}} \right]_{3 \times 2}}{\left[ {\begin{array}{*{20}{c}}{ - 4}&{ - 5}&{ - 6}\\0&0&1\end{array}} \right]_{2 \times 3}}$
$P = {\left[ {\begin{array}{*{20}{c}}{ - 3}&{ - 14}\\{ - 8}&{ - 20}\\{ - 11}&{ - 26}\end{array}} \right]_{3 \times 2}}{\left[ {\begin{array}{*{20}{c}}{ - 4}&{ - 5}&{ - 6}\\0&0&1\end{array}} \right]_{2 \times 3}}$
$P = {\left[ {\begin{array}{*{20}{c}}{12}&{15}&4\\{32}&{40}&{28}\\{44}&{55}&{40}\end{array}} \right]_{3 \times 3}}$$ \Rightarrow $ ${P_{22}} = 40$.

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