Find X if 2 X-3 Y- begin bmatrix 2 - 3 1480lendbmatrix and7 -2 1-1 - 5 l e n d b m a t r i x A- frac -25- frac -135 1 frac -145- 2lendbmatrix frac -25- frac 125frac115-3lendbmatrix C- Veginbmatrix frac25- frac -125- frac -115- 3lendbmatrix D- beginbmatrix frac25- frac 135 1 frac 145-2 e n d b m a t r i x

The correct option is C [ 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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Byju's Answer

Standard IX

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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Similar questions

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

If $A = [\begin{matrix} 5 & 4 3 & - 1 \end{matrix}], B = [\begin{matrix} 2 & 1 0 & 4 \end{matrix}]$ and $C = [\begin{matrix} - 3 & 2 1 & 0 \end{matrix}]$ then find A + B - C

Q. Match the following

\begin{matrix} Column A & Column B 1. A = {x : x is an odd natural number} & a . {\frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{3}{4}, \frac{3}{5}, \frac{5}{7}} 2. B = {x : x = (n^{2})}, n \in N and x < 100 & b . {1, 4, 9, 16, 25, . . . . . . . .10000} 3. C = {x : x = \frac{n}{n + 2}, where n is a natural number and 1 \leq n \leq 6} & c . {1, 4, 9, 16, 25, 36, 49, 64, 81} 4. D = {x : x is a letter of the word TRIGONOMETRY} & d . {G, E, I, M, N, O, R, T, Y} e . {1, 3, 5, 7, 9, . . . . . . . . . . . . . . .} \end{matrix}

Q. If

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