If A=3 2 −11 5 4−2 3 7,B=1 2 12 1 21 2 1 and 3A + 2X= 5B then X is

3A+2X=5B⇒2λ=5B−3A=5105105105105−96−331512−6921⇒X=12−4487−10−2111−16=−2247/2−5−111/21/2−8

If A=3 2 −11 5 4−2 3 7,B=1 2 12 1 21 2 1 and 3A + 2X= 5B then X is

3A+2X=5B⇒2λ=5B−3A=5105105105105−96−331512−6921⇒X=12−4487−10−2111−16=−2247/2−5−111/21/2−8

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If $A = [\begin{array}{rrr} 3 2 - 1 \\ 1 5 4 \\ - 2 3 7 \end{array}], B = [\begin{array}{lll} 1 2 1 \\ 2 1 2 \\ 1 2 1 \end{array}]$ and 3A + 2X= 5B then X is

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$[\begin{array}{rr} 0 - 2 \\ 3 7 \\ 5 6 \end{array}]$

$[\begin{array}{rr} 4 / 5 1 \\ 9 / 5 - 2 / 5 \\ - 4 / 5 - 3 / 5 \end{array}]$

$[\begin{array}{rrr} - 2 2 4 \\ 7 / 2 - 5 - 1 \\ 11 / 2 1 / 2 - 8 \end{array}]$

$[\begin{array}{ll} 0 2 \\ 3 7 \\ 5 6 \end{array}]$

answer is C.

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Detailed Solution

$\begin{array}{l} 3 A + 2 X = 5 B \Rightarrow 2 λ = 5 B - 3 A = [\begin{array}{ccc} 5 & 10 & 5 \\ 10 & 5 & 10 \\ 5 & 10 & 5 \end{array}] - [\begin{array}{ccc} 9 & 6 & - 3 \\ 3 & 15 & 12 \\ - 6 & 9 & 21 \end{array}] \\ \Rightarrow X = \frac{1}{2} [\begin{array}{rrr} - 4 & 4 & 8 \\ 7 & - 10 & - 2 \\ 11 & 1 & - 16 \end{array}] = [\begin{array}{rrr} - 2 & 2 & 4 \\ 7 / 2 & - 5 & - 1 \\ 11 / 2 & 1 / 2 & - 8 \end{array}] \end{array}$