tentukan determinan,adjoin dan invers dari matriks berikut! c.(-1. 3. ) (4. -6 )

Materi Matriks
Kelas X

C = [tex] \left(\begin{array}{cc} -1 & 3 \\ 4 & -6 \end{array}\right) [/tex]

a. |C| = (-1)(-6) - (3)(4)
|C| = 6 - 12 = -6

m₁₁ = -6
m₁₂ = 4
m₂₁ = 3
m₂₂ = -1

Minor = [tex] \left(\begin{array}{cc} -6 & 4 \\ 3 & -1 \end{array}\right) [/tex]

c₁₁ = (-1)¹⁺¹ • (-6) = -6
c₁₂ = (-1)¹⁺² • 4 = -4
c₂₁ = (-1)²⁺¹ • 3 = -3
c₂₂ = (-1)²⁺² • (-1) = -1

Kofaktor = [tex] \left(\begin{array}{cc} -6 & -4 \\ -3 & -1 \end{array}\right) [/tex]

b. Adjoint = [tex] \left(\begin{array}{cc} -6 & -3 \\ -4 & -1 \end{array}\right) [/tex]

c. C⁻¹ = (1 / |C|) • Adj. C
C⁻¹ = ¹/₋₆ • [tex] \left(\begin{array}{cc} -6 & -3 \\ -4 & -1 \end{array}\right) [/tex]
C⁻¹ = [tex] \left(\begin{array}{cc} 1 & \frac12 \\ \frac23 & \frac16 \end{array}\right) [/tex]