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Mathematics

If [2004][xy]\begin{bmatrix} 2 & 0 \ 0 & 4 \end{bmatrix}\begin{bmatrix} x \ y \end{bmatrix} = [28]\begin{bmatrix} 2 \ -8 \end{bmatrix}, the values of x and y respectively are:

  1. 1, -2

  2. -2, 1

  3. 1, 2

  4. -2, -1

Matrices

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Answer

Given,

[2004][xy]\begin{bmatrix} 2 & 0 \ 0 & 4 \end{bmatrix}\begin{bmatrix} x \ y \end{bmatrix} = [28]\begin{bmatrix} 2 \ -8 \end{bmatrix}

Solving,

[2(x)+0(y)0(x)+4(y)]=[28][2x4y]=[28]\Rightarrow \begin{bmatrix} 2(x) + 0(y) \ 0(x) + 4(y) \end{bmatrix}= \begin{bmatrix} 2 \ -8 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 2x \ 4y \end{bmatrix}= \begin{bmatrix} 2 \ -8 \end{bmatrix}

∴ 2x = 2

⇒ x = 22\dfrac{2}{2}

⇒ x = 1.

∴ 4y = -8

⇒ y = 84\dfrac{-8}{4}

⇒ y = -2.

Hence, option 1 is the correct option.

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