invers dari matriks P=[(1 1)(4 −2)] adalah ...

Jawaban : [(1/3 1/6)(2/3 −1/6)] Pembahasan : Konsep : A = [(a b)(c d)] maka det A = |(a b)(c d)| = ad − bc adjoin A = [(d −b)(−c a)] A⁻¹ = 1/(det A) . adjoin A dimana A⁻¹ : invers A P = [(1 1)(4 −2)] det P = |(1 1)(4 −2)| = (1)(−2) − (4)(1) = −2 − 4 = −6 adjoin P = [(−2 −1)(−4 1)] Maka P⁻¹ = 1/(det P) . adjoin P = 1/(−6) . [(−2 −1)(−4 1)] = [(−2/(−6) −1/(−6))(−4/(−6) 1/(−6))] = [(1/3 1/6)(4/6 −1/6)] = [(1/3 1/6)(2/3 −1/6)] Jadi, invers dari matriks P=[(1 1)(4 −2)] adalah [(1/3 1/6)(2/3 −1/6)]