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Evaluate the Following Determinant: ∣ ∣ ∣ ∣ 6 − 3 2 2 − 1 2 − 10 5 2 ∣ ∣ ∣ ∣

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Question

Evaluate the following determinant:

\[\begin{vmatrix}6 & - 3 & 2 \\ 2 & - 1 & 2 \\ - 10 & 5 & 2\end{vmatrix}\]

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Solution

\[ ∆ = \begin{vmatrix}6 & - 3 & 2 \\ 2 & - 1 & 2 \\ - 10 & 5 & 2\end{vmatrix}\]
\[ = 6( - 2 - 10) - ( - 3)(4 + 20) + 2(10 - 10)\]
\[ = - 72 + 72 + 0\]
\[ = - 72 + 72\]
\[ = 0\]

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Chapter 5: Determinants - Exercise 6.2 [Page 57]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 5 Determinants
Exercise 6.2 | Q 1.6 | Page 57
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