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Mathematics

If [x+2y3y4x2]=[0382],\begin{bmatrix}[r] x + 2y & 3y \ 4x & 2 \end{bmatrix} = \begin{bmatrix}[r] 0 & -3 \ 8 & 2 \end{bmatrix}, then the value of x - y is

  1. -3
  2. 1
  3. 3
  4. 5

Matrices

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Answer

Given,

[x+2y3y4x2]=[0382]\begin{bmatrix}[r] x + 2y & 3y \ 4x & 2 \end{bmatrix} = \begin{bmatrix}[r] 0 & -3 \ 8 & 2 \end{bmatrix} \\[0.5em]

By definition of equality of matrices we get,

⇒ x + 2y = 0     (…Eq 1)

⇒ 3y = -3 or y = -1

⇒ 4x = 8 or x = 2

Putting the value of x = 2 and y = -1 in Eq 1

⇒ x + 2y = 0
⇒ L.H.S. = 2 + 2(-1) = 2 - 2 = 0 = R.H.S.

Since, x = 2 and y = -1 satisfies Eq 1

∴ x = 2, y = -1 and x - y = 2 - (-1) = 2 + 1 = 3.

∴ Option 3 is the correct option.

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