If A + B = [ * 20 c 1&0 1&1 ]and A - 2B = [ * 20 c - 1 &1 0& - 1 … - Vidyadip

MCQ

If $A + B = \left[ {\begin{array}{*{20}{c}}1&0\\1&1\end{array}} \right]$and $A - 2B = \left[ {\begin{array}{*{20}{c}}{ - 1}&1\\0&{ - 1}\end{array}} \right]\,,$ then $A=$

A
$\left[ {\begin{array}{*{20}{c}}1&1\\2&1\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}{2/3}&{1/3}\\{1/3}&{2/3}\end{array}} \right]$
✓
$\left[ {\begin{array}{*{20}{c}}{1/3}&{1/3}\\{2/3}&{1/3}\end{array}} \right]$
D
None of these

✓

Answer

Correct option: C.

$\left[ {\begin{array}{*{20}{c}}{1/3}&{1/3}\\{2/3}&{1/3}\end{array}} \right]$

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

On adding, we get$3A = \left[ {\begin{array}{*{20}{c}}1&1\\2&1\end{array}} \right]$

$ \Rightarrow \,A = \left[ {\begin{array}{*{20}{c}}{1/3}&{1/3}\\{2/3}&{1/3}\end{array}} \right]$.

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