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Mathematics

If 2[345x]+[1y01]=[70105]2\begin{bmatrix} 3 & 4 \ 5 & x \end{bmatrix} + \begin{bmatrix} 1 & y \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 7 & 0 \ 10 & 5 \end{bmatrix}, then the value of (x – y) is:

  1. 10

  2. -10

  3. 6

  4. -6

Matrices

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Answer

Given,

2[345x]+[1y01]=[70105]2\begin{bmatrix} 3 & 4 \ 5 & x \end{bmatrix} + \begin{bmatrix} 1 & y \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 7 & 0 \ 10 & 5 \end{bmatrix}

Solving:

⇒[68102x]+[1y01]=[70105]⇒[6+18+y10+02x+1]=[70105]⇒[78+y102x+1]=[70105].\Rightarrow \begin{bmatrix} 6 & 8 \ 10 & 2x \end{bmatrix} + \begin{bmatrix} 1 & y \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 7 & 0 \ 10 & 5 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 6 + 1 & 8 + y \ 10 + 0 & 2x + 1 \end{bmatrix} = \begin{bmatrix} 7 & 0 \ 10 & 5 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 7 & 8 + y \ 10 & 2x + 1 \end{bmatrix} = \begin{bmatrix} 7 & 0 \ 10 & 5 \end{bmatrix}.

∴ 8 + y = 0

⇒ y = -8

∴ 2x + 1 = 5

⇒ 2x = 5 - 1

⇒ 2x = 4

⇒ x = 42\dfrac{4}{2}

⇒ x = 2

∴ x - y = 2 - (-8) = 10

Hence, option 1 is the correct option.

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