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If ∣ ∣ ∣ ∣ a P X B Q Y C R Z ∣ ∣ ∣ ∣ = 16 , Then the Value of ∣ ∣ ∣ ∣ P + X a + X a + P Q + Y B + Y B + Q R + Z C + Z C + R ∣ ∣ ∣ ∣ is (A) 4 (B) 8 (C) 16 (D) 32 - Mathematics

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प्रश्न

If \[\begin{vmatrix}a & p & x \\ b & q & y \\ c & r & z\end{vmatrix} = 16\] , then the value of \[\begin{vmatrix}p + x & a + x & a + p \\ q + y & b + y & b + q \\ r + z & c + z & c + r\end{vmatrix}\] is

विकल्प

  • 4

  • 8

  • 16

  • 32

MCQ
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उत्तर

\[\begin{vmatrix}p + x & a + x & a + p \\ q + y & b + y & b + q \\ r + z & c + z & c + r\end{vmatrix} = \begin{vmatrix}p & a & a \\ q & b & b \\ r & c & c\end{vmatrix} + \begin{vmatrix}p & a & p \\ q & b & q \\ r & c & r\end{vmatrix} + \begin{vmatrix}p & x & a \\ q & y & b \\ r & z & c\end{vmatrix} + \begin{vmatrix}p & x & p \\ q & y & q \\ r & z & r\end{vmatrix} + \begin{vmatrix}x & a & a \\ y & b & b \\ z & c & c\end{vmatrix} + \begin{vmatrix}x & a & p \\ y & b & q \\ z & c & r\end{vmatrix} + \begin{vmatrix}x & x & a \\ y & y & b \\ z & z & c\end{vmatrix} + \begin{vmatrix}x & x & p \\ y & y & q \\ z & z & r\end{vmatrix}\]
\[ = 0 + 0 + \begin{vmatrix}p & x & a \\ q & y & b \\ r & z & c\end{vmatrix} + 0 + 0 + \begin{vmatrix}x & a & p \\ y & b & q \\ z & c & r\end{vmatrix} + 0 + 0\]
\[ = \begin{vmatrix}p & x & a \\ q & y & b \\ r & z & c\end{vmatrix} + \begin{vmatrix}x & a & p \\ y & b & q \\ z & c & r\end{vmatrix}\]
\[ = 2\begin{vmatrix}a & p & x \\ b & q & y \\ c & r & z\end{vmatrix}\]
\[ = 2 \times 16 = 32\]

 

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अध्याय 6: Determinants - Exercise 6.7 [पृष्ठ ९६]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 6 Determinants
Exercise 6.7 | Q 32 | पृष्ठ ९६

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