1. Diberikan matriks \( A = \begin{pmatrix}-1 & 3 & 2 \\ 2 & 1 & 3 \\ 1 & 2 & 1\end{pmatrix} \). \n2. Kita diminta mencari determinan matriks \( A \). \n3. Determinan matriks 3x3 dihitung dengan rumus: $$\det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$ Dimana elemen matriks: \( A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} \) Jadi: \(a = -1, b = 3, c = 2, d = 2, e = 1, f = 3, g = 1, h = 2, i = 1\). 4. Hitung setiap bagian: - \(ei - fh = 1 \times 1 - 3 \times 2 = 1 - 6 = -5\) - \(di - fg = 2 \times 1 - 3 \times 1 = 2 - 3 = -1\) - \(dh - eg = 2 \times 2 - 1 \times 1 = 4 - 1 = 3\) 5. Substitusikan ke rumus determinan: $$\det(A) = (-1)(-5) - 3(-1) + 2(3) = 5 + 3 + 6 = 14$$ 6. Jadi, determinan matriks \( A \) adalah \(14\).