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Mathematics

If [x+27y+3a2]=[4b343]\begin{bmatrix}[r] x + 2 & 7 \ y + 3 & a - 2 \end{bmatrix} = \begin{bmatrix}[r] 4 & b - 3 \ 4 & 3 \end{bmatrix}, the value of x, y, a and b are :

  1. x = 2, y = 1, a = 5 and b = 10

  2. x = -2, y = 1, a = 5 and b = 10

  3. x = 2, y = -1, a = 5 and b = 10

  4. x = 2, y = 1, a = -5 and b = 10

Matrices

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Answer

Given,

[x+27y+3a2]=[4b343]\begin{bmatrix}[r] x + 2 & 7 \ y + 3 & a - 2 \end{bmatrix} = \begin{bmatrix}[r] 4 & b - 3 \ 4 & 3 \end{bmatrix}.

∴ x + 2 = 4

⇒ x = 4 - 2 = 2.

∴ y + 3 = 4

⇒ y = 4 - 3 = 1.

∴ b - 3 = 7

⇒ b = 7 + 3 = 10.

∴ a - 2 = 3

⇒ a = 3 + 2 = 5.

Hence, Option 1 is the correct option.

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