Answered

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find the
-2
-4
-3
-1
-9-8
determinant OF
-15
- 5
6

Sagot :

LammettHash

Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix

[tex]A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}[/tex]

Let's compute the determinant by taking the cofactor expansion along the first column:

[tex]\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}[/tex]

[tex]\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))[/tex]

[tex]\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)[/tex]

[tex]\det A = \boxed{74}[/tex]

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