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Mathematics

If [a+b25ab]=[6258]\begin{bmatrix} a + b & 2 \ 5 & ab \end{bmatrix} = \begin{bmatrix} 6 & 2 \ 5 & 8 \end{bmatrix}, then the values of a and b are:

  1. a = 4, b = 2

  2. a = 2, b = 4

  3. both (a) and (b)

  4. none of these

Matrices

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Answer

Given,

[a+b25ab]=[6258]\begin{bmatrix} a + b & 2 \ 5 & ab \end{bmatrix} = \begin{bmatrix} 6 & 2 \ 5 & 8 \end{bmatrix}

∴ a + b = 6

⇒ b = 6 - a…(1)

∴ ab = 8…(2)

Substituting value of b from equation(1) in ab = 8, we get:

⇒ a (6 - a) = 8

⇒ 6a - a2 = 8

⇒ a2 - 6a + 8 = 0

⇒ a2 - 4a - 2a + 8 = 0

⇒ a(a - 4) -2(a - 4) = 0

⇒ (a - 2)(a - 4) = 0

(a - 2)= 0 or (a - 4) = 0 [Using zero product rule]

⇒ a = 2 or a = 4

If a = 2, then b = 6 − 2 = 4.

If a = 4, then b = 6 − 4 = 2.

Hence, option 3 is the correct option.

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