If A=−12−21, B=342−1 and A + 2X= B then X=

A=-12-21 B=342-1 A+2X=B2X=B−A2X=342-1−-12-212X=424-2 X=12424-2X=212-1

If A=−12−21, B=342−1 and A + 2X= B then X=

A=-12-21 B=342-1 A+2X=B2X=B−A2X=342-1−-12-212X=424-2 X=12424-2X=212-1

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If $A = [\begin{matrix} - 1 & 2 \\ - 2 & 1 \end{matrix}], B = [\begin{matrix} 3 & 4 \\ 2 & - 1 \end{matrix}]$ and $A + 2 X = B$ then X=

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$[\begin{matrix} 2 & 1 \\ - 2 & - 1 \end{matrix}]$

$[\begin{matrix} 2 & 1 \\ 2 & - 1 \end{matrix}]$

$[\begin{matrix} 2 & - 1 \\ 2 & 1 \end{matrix}]$

$[\begin{matrix} - 2 & - 1 \\ - 2 & 1 \end{matrix}]$

answer is B.

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Detailed Solution

$\begin{array}{rcl} A & = & [\begin{matrix} - 1 & 2 \\ - 2 & 1 \end{matrix}] B = [\begin{matrix} 3 & 4 \\ 2 & - 1 \end{matrix}] \\ A + 2 X & = & B \\ 2 X & = & B - A \\ 2 X & = & [\begin{matrix} 3 & 4 \\ 2 & - 1 \end{matrix}] - [\begin{matrix} - 1 & 2 \\ - 2 & 1 \end{matrix}] \\ 2 X & = & [\begin{matrix} 4 & 2 \\ 4 & - 2 \end{matrix}] \begin{matrix} \end{matrix} \\ X & = & \frac{1}{2} [\begin{matrix} 4 & 2 \\ 4 & - 2 \end{matrix}] \\ X & = & [\begin{matrix} 2 & 1 \\ 2 & - 1 \end{matrix}] \end{array}$