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Mathematics

If [pq2q2q+rp+q]=[1495]\begin{bmatrix} p - q & 2q \ 2q + r & p + q \end{bmatrix} = \begin{bmatrix} 1 & 4 \ 9 & 5 \end{bmatrix}, then the value of (p + q + r) is:

  1. 8

  2. 10

  3. -5

  4. -10

Matrices

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Answer

[pq2q2q+rp+q]=[1495]\begin{bmatrix} p - q & 2q \ 2q + r & p + q \end{bmatrix} = \begin{bmatrix} 1 & 4 \ 9 & 5 \end{bmatrix}

Solving for p, q and r:

∴ 2q = 4…(1)

⇒ q = 42\dfrac{4}{2}

⇒ q = 2.

∴ p - q = 1

⇒ p - 2 = 1

⇒ p = 1 + 2

⇒ p = 3.

∴ 2q + r = 9

⇒ 2(2) + r = 9

⇒ 4 + r = 9

⇒ r = 9 - 4

⇒ r = 5.

∴ p + q + r = 3 + 2 + 5 = 10.

Hence, option 2 is the correct option.

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