Question

A3 = 2 1 -1 -2
3 -2 -1 -1
2 -5 -1 0
-4 0 3 0

Determinan matriks A3 dengan metode minor kofaktor

Answer 1

Dengan menggunakan metode minor dan kofaktor.

Menggunakan minor di baris pertama:
Dengan:
M₁₁ = 2
M₁₂ = 1
M₁₃ = -1
M₁₄ = 2

Serta, matriks kofaktornya:
C₁₁ = (-1)¹⁺¹ [-2 -1 -1 \\ -5 -1 0 \\ 0 3 0] = 1 x (-15) = -15
C₁₂ = (-1)¹⁺² [3 -1 -1 \\ 2 -1 0 \\ -4 3 0] = (-1) x (-2) = 2
C₁₃ = (-1)¹⁺³ [3 -2 -1 \\ 2 -5 0 \\ -4 0 0] = 1 x 20 = 20
C₁₄ = (-1)¹⁺⁴ [3 -2 -1 \\ 2 -5 -1 \\ -4 0 3] = (-1) x (-21) = 21

Maka, determinannya adalah
= M₁₁C₁₁ + M₁₂C₁₂ + M₁₃C₁₃ + M₁₄C₁₄
= -30 + 2 - 20 + 42
= -6