Let A + 2B = [ * 20 c 1&2&0 6& - 3 &3 - 5 &3&1 ] and 2A - B = [ *… - Vidyadip

Question

Let $A + 2B =$ $\left[ {\begin{array}{*{20}{c}}1&2&0\\6&{ - 3}&3\\{ - 5}&3&1 \end{array}} \right]$ and $2A - B =$ $\left[ {\begin{array}{*{20}{c}}2&{ - 1}&5\\ 2&{ - 1}&6\\0&1&2\end{array}} \right]$ then $Tr (A) - Tr (B)$ has the value equal to

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Answer

c
$t_r(A) + 2 t_r(B) = - 1$ (from the given matrix)
and $2 t_r(A) - t_r(B) = 3$ (from the given matrix)
Let $t_r(A) = x$ and $t_r(B) = y$
$x + 2y = - 1$
$2x - y = 3$
solving $x = 1$ and $y = - 1$
Hence $t_r(A) - t_r(B) = x - y = 2$

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