Diketahui P = (3 1)
(-1 2)
tentukan hasil dari m...

Question

Diketahui P = (3    1)
                           (-1   2)  
tentukan hasil dari matriks P-¹ !

E. Aritonang · Accepted Answer

Hai Emmanuela, jawaban soal ini adalah P^(-1) = [(2/7 -1/7) (1/7 3/7)]

Matriks A = [(a b) (c d)], maka :
• |A| = ad - bc
• A^(-1) = (1/|A|) [(d -b) (-c a)]
• kA =[(ka kb) (kc kd)]
Dengan k = skalar

Matriks P = [(3 1) (-1 2)]
---> a = 3, b = 1, c = -1, d = 2

>> |P| = ad - bc
= 3(2) - 1(-1) 
= 6 + 1
= 7

>> P^(-1) = (1/|P|) [(d - b) (-c a)]
= (1/7) [(2 -1) (-(-1) 3)]
= (1/7) [(2 -1) (1 3)]
= [(2/7  -1/7) (1/7  3/7)]

Maka, hasil dari matriks P^(-1) = [(2/7 -1/7) (1/7 3/7)].

Semoga membantu ya.

Diketahui P = (3 1) (-1 2) tentukan hasil dari matriks P-¹ !