Let $2A+B = left[ {begin{array}{*{20}{c}} 1&0&3 { - 1}&4&6

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3 and 4 .Determinants and Matrices

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Let $2A+B = \left[ {\begin{array}{{20}{c}}
1&0&3 \\
{ - 1}&4&6 \\
2&5&2
\end{array}} \right],\,A - 2B = \left[ {\begin{array}{{20}{c}}
2&{ - 1}&5 \\
0&3&6 \\
1&2&1
\end{array}} \right]$ . Then $Tr(A) -Tr(B)$ has the value equal to (where $Tr(A)$ denotes the trace of matrix $A$)

A

$3$

B

$5$

C

$6$

D

$7$

Solution

$2Tr(A) + Tr(B) = 7$
and $Tr(A)\ -2Tr(B) = 6$
$\Rightarrow Tr(A) = 4\ and\ Tr(B) =\ -1$

Standard 12

Mathematics

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