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Write the Value of the Determinant ∣ ∣ ∣ ∣ 2 − 3 5 4 − 6 10 6 − 9 15 ∣ ∣ ∣ ∣ . - Mathematics

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Question

Write the value of the determinant \[\begin{vmatrix}2 & - 3 & 5 \\ 4 & - 6 & 10 \\ 6 & - 9 & 15\end{vmatrix} .\]

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Solution

\[A = \begin{vmatrix} 2 & - 3 & 5\\4 & - 6 & 10\\6 & - 9 & 15 \end{vmatrix}\] 
\[ = \begin{vmatrix} 2 & - 3 & 5\\4 - 4 & - 6 + 6 & 10 - 10\\6 & - 9 & 15 \end{vmatrix} \left[\text{ Applying }R_2 \to R_2 - 2R {}_1 \right]\] 
\[ = \begin{vmatrix} 2 & - 3 & 5\\0 & 0 & 0\\6 & - 9 & 15 \end{vmatrix} \] 
\[ = 0\] 

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Chapter 6: Determinants - Exercise 6.6 [Page 91]

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RD Sharma Mathematics [English] Class 12
Chapter 6 Determinants
Exercise 6.6 | Q 27 | Page 91

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