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Mathematics

If [x2y53y]=[6532],\begin{bmatrix}[r] x - 2y & 5 \ 3 & y \end{bmatrix} = \begin{bmatrix}[r] 6 & 5 \ 3 & -2 \end{bmatrix}, then the value of x is

  1. -2
  2. 0
  3. 1
  4. 2

Matrices

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Answer

Given,

[x2y53y]=[6532]\begin{bmatrix}[r] x - 2y & 5 \ 3 & y \end{bmatrix} = \begin{bmatrix}[r] 6 & 5 \ 3 & -2 \end{bmatrix} \\[0.5em]

By definition of equality of matrices,

⇒ x - 2y = 6     (…Eq 1)

⇒ y = -2.

Putting value of y in Eq 1 we get,

⇒ x - 2y = 6
⇒ x - 2(-2) = 6
⇒ x + 4 = 6
⇒ x = 6 - 4
⇒ x = 2.

∴ x = 2.

∴ Option 4 is the correct option .

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