Evaluate the determinant of the matrix M = \(\begin{bmatrix}3 & 4 & 6\\2 & 1 & -1\\-1 & 3 & 5\end{bmatrix}\)
- 20
- 25
-
30
- 35
The correct answer is: C
Explanation
M = \(\begin{bmatrix}3 & 4 & 6\\2 & 1 & -1\\-1 & 3 & 5\end{bmatrix}\)
|M| = 3\(\begin{bmatrix}1 & -1\\3 & 5\end{bmatrix}\) - 4\(\begin{bmatrix}2 & -1\\-1 & 5\end{bmatrix}\) + 6\(\begin{bmatrix}2 & 1\\-1 & 3\end{bmatrix}\)
3(5 + 3) - 4(10 - 1) + 6(6 + 1) = 24 - 36 + 42 = 30
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