Find X if 2 X-3 Y- begin bmatrix 2 - 3 1480lendbmatrix and7 -2 l-1 - 5 l e n d b m a t r i x A- frac25-frac-125-frac-115lendbmatrix frac25-frac145-2lendbmatrix C- Veginbmatrix frac-25-frac-145- 2lendbmatrix D- beginbmatrix frac -25- frac 125 frac 115-3 e n d b m a t r i x

The correct option is A [ 2/5 amp; 12/5; 11/5 amp; 3 ] 2X+3Y=[ 2 amp;3; 4 amp;0 ]........(i) 3X+2Y=[ 2 amp; 2; 1 amp;5 ]..... ...

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Standard XII

Mathematics

Addition and Subtraction of a Matrix

Find X if 2 X...

Question

Find X if $2 X + 3 Y = [\begin{matrix} 2 & 3 4 & 0 \end{matrix}] a n d 3 X + 2 Y = [\begin{matrix} 7 & - 2 - 1 & 5 \end{matrix}]$

$⎡ ⎣ \begin{matrix} \frac{- 2}{5} & \frac{12}{5} \frac{11}{5} & - 3 \end{matrix} ⎤ ⎦$

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$⎡ ⎣ \begin{matrix} \frac{2}{5} & \frac{- 12}{5} \frac{- 11}{5} & 3 \end{matrix} ⎤ ⎦$

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$⎡ ⎣ \begin{matrix} \frac{2}{5} & \frac{13}{5} \frac{14}{5} & - 2 \end{matrix} ⎤ ⎦$

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$⎡ ⎣ \begin{matrix} \frac{- 2}{5} & \frac{- 13}{5} \frac{- 14}{5} & 2 \end{matrix} ⎤ ⎦$

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Solution

The correct option is B
$⎡ ⎣ \begin{matrix} \frac{2}{5} & \frac{- 12}{5} \frac{- 11}{5} & 3 \end{matrix} ⎤ ⎦$

$2 X + 3 Y = [\begin{matrix} 2 & 3 4 & 0 \end{matrix}] . . . . . . . . (i) 3 X + 2 Y = [\begin{matrix} 2 & - 2 - 1 & 5 \end{matrix}] . . . . . . . . (i i) (i) \times 2 \Rightarrow 4 X + 6 Y = [\begin{matrix} 4 & 6 8 & 0 \end{matrix}] . . . . . . . . (i i i) (i i) \times 3 \Rightarrow 9 X + 6 Y = [\begin{matrix} 6 & - 6 - 3 & 15 \end{matrix}] . . . . . . . . (i v) (i v) - (i i i) \Rightarrow 5 X = [\begin{matrix} 2 & - 12 - 11 & 15 \end{matrix}] x = ⎡ ⎣ \begin{matrix} \frac{2}{5} & \frac{- 12}{5} \frac{- 11}{5} & 3 \end{matrix} ⎤ ⎦$

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Find X if 2X+3Y=[2340]and 3X+2Y=[7−2−15]

The correct option is B ⎡⎣25−125−1153⎤⎦ 2X+3Y=[2340]........(i)3X+2Y=[2−2−15]........(ii)(i)×2⇒4X+6Y=[4680]........(iii)(ii)×3⇒9X+6Y=[6−6−315]........(iv)(iv)−(iii)⇒5X=[2−12−1115]x=⎡⎣25−125−1153⎤⎦

Find X if $2 X + 3 Y = [\begin{matrix} 2 & 3 4 & 0 \end{matrix}] a n d 3 X + 2 Y = [\begin{matrix} 7 & - 2 - 1 & 5 \end{matrix}]$