Find X and y-if lbeginbmatrix 2 x - x 1y - 3 ylendbmatrix bmatrix 3112end bmatrix - begin bmatrix 16 19lendbmatrix - A- x-2- y-1B- x-2- y-1C- x-2- y-1D- x-2- y-2

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Equality of Matrices

Find X and y,...

Question

Find $x$ and $y$ ,
$i f [\begin{matrix} 2 x & x y & 3 y \end{matrix}] [\begin{matrix} 32 \end{matrix}] = [\begin{matrix} 169 \end{matrix}] .$

x = -2, y = 1

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x = 2, y = -1

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x = 2, y = 1

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x = 2, y = 2

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Solution

The correct option is C x = 2, y = 1
To find the values of $x$ and $y$ , we will first find the product of the matrices and then, compare the values.
$[\begin{matrix} 2 x & x y & 3 y \end{matrix}] [\begin{matrix} 32 \end{matrix}] = [\begin{matrix} 169 \end{matrix}]$

$\Rightarrow [\begin{matrix} 8 x 9 y \end{matrix}] = [\begin{matrix} 169 \end{matrix}]$

$\begin{matrix} S o, & 8 x = 16 \Rightarrow & x = 2 \end{matrix} ∣ ∣ ∣ \begin{matrix} 9 y = 9 \Rightarrow & y = 1 \end{matrix}$

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Q. If

[\begin{matrix} x + y & y 2 x & x - y \end{matrix}] [\begin{matrix} 2 - 2 \end{matrix}] = [\begin{matrix} 32 \end{matrix}]

then

x - y

is equal to

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Find x and y, if [2xxy3y][32]=[169].

The correct option is C x = 2, y = 1To find the values of x and y, we will first find the product of the matrices and then, compare the values. [2xxy3y][32]=[169] ⇒[8x9y]=[169] So,8x=16⇒x=2∣∣∣ 9y=9⇒y=1

Find $x$ and $y$ ,
$i f [\begin{matrix} 2 x & x y & 3 y \end{matrix}] [\begin{matrix} 32 \end{matrix}] = [\begin{matrix} 169 \end{matrix}] .$