MathematicsIf A+2B=1206−33−531, and 2A−B=2−152−16012, then tr(A)−tr(B) is

If $A + 2 B = [\begin{array}{l} 1 & 2 & 0 \\ 6 & - 3 & 3 \\ - 5 & 3 & 1 \end{array}]$ , and $2 A - B = [\begin{array}{l} 2 & - 1 & 5 \\ 2 & - 1 & 6 \\ 0 & 1 & 2 \end{array}]$ , then $tr (A) - tr (B)$ is

$A + 2 B = [\begin{array}{l} 1 & 2 & 0 \\ 6 & - 3 & 3 \\ - 5 & 3 & 1 \end{array}]$

$tr (A + 2 B) = - 1$

$tr (A) + 2 tr (B) = - 1$

$2 A - B = [\begin{array}{l} 2 & - 1 & 5 \\ 2 & - 1 & 6 \\ 0 & 1 & 2 \end{array}]$

$tr (2 A - B) = 3$

$2 tr (A) - tr (B) = 3$

Solving (1) and (2), we get $tr (A) = 1, tr (B) = - 1$

$tr (A) - tr (B) = 2$

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