If A=4101-22, B=20-1314, C=12-1 and (3B–2A) C+2X=O then X =

A=4101-22, B=20-1314, C=12-1 3B-2A=-2-2-3778 (3B-2A)C=-2-2-3778 12-1 =-313 ∴ 2x=-(3B-2A)C =-313 x=12-313

If A=4101-22, B=20-1314, C=12-1 and (3B–2A) C+2X=O then X =

A=4101-22, B=20-1314, C=12-1 3B-2A=-2-2-3778 (3B-2A)C=-2-2-3778 12-1 =-313 ∴ 2x=-(3B-2A)C =-313 x=12-313

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If $A = (\begin{matrix} 4 & 1 & 0 \\ 1 & - 2 & 2 \end{matrix}), B = (\begin{matrix} 2 & 0 & - 1 \\ 3 & 1 & 4 \end{matrix}), C = (\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix})$ and (3B–2A) C+2X=O then X =

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$\frac{1}{2} [\begin{matrix} 3 \\ 13 \end{matrix}]$

$\frac{1}{2} [\begin{matrix} 3 \\ - 13 \end{matrix}]$

$\frac{1}{2} [\begin{matrix} - 3 \\ 13 \end{matrix}]$

$[\begin{matrix} 3 \\ - 13 \end{matrix}]$

answer is C.

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Detailed Solution

$A = (\begin{matrix} 4 & 1 & 0 \\ 1 & - 2 & 2 \end{matrix}), B = (\begin{matrix} 2 & 0 & - 1 \\ 3 & 1 & 4 \end{matrix}), C = (\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix}) 3 B - 2 A = [\begin{matrix} - 2 & - 2 & - 3 \\ 7 & 7 & 8 \end{matrix}] (3 B - 2 A) C = [\begin{matrix} - 2 & - 2 & - 3 \\ 7 & 7 & 8 \end{matrix}] (\begin{matrix} 1 \\ 2 \\ - 1 \end{matrix}) = [\begin{matrix} - 3 \\ 13 \end{matrix}] ∴ 2 x = - (3 B - 2 A) C = [\begin{matrix} - 3 \\ 13 \end{matrix}] x = \frac{1}{2} [\begin{matrix} - 3 \\ 13 \end{matrix}]$