Jika A=[(0 1 5)(0 0 1)(0 0 0)], maka A^(2016)=… A. [(0 0 0)(0 0 0)(0 0 0)] B. [(0 1 0)(0 0 1)(0 0 0)] C. [(0 1 5)(0 0 1)(0 0 0)] D. [(0 2016 5)(0 0 2016)(0 0 0)] E. [(0 1 5^(2016))(0 0 1)(0 0 0)]

Halo Mahkota D, kakak bantu jawab ya :) Jawbannya adalah A. [(0 0 0)(0 0 0)(0 0 0)] Untuk menghitung matriks 3 x 3 dengan A = [(a b c)(d e f)(g h i)] dan B = [(p q r)(s t u)(v w x)] maka A x B = [(ap+bs+cv aq+bt+cw ar+bu+cx) (dp+es+fv dq+et+fw dr+eu+fx) (gp+hs+iv gq+ht+iw gr+hu+ix) Diketahui A=[(0 1 5)(0 0 1)(0 0 0)] Sekarang kita hitung nilai A^2 A^2 = A x A A^2 = [(0 1 5)(0 0 1)(0 0 0)] [(0 1 5)(0 0 1)(0 0 0)] A^2 = [(0x0+1x0+5x0 0x1+1x0+5x0 0x5+1x1+5x0) (0x0+0x0+1x0 0x1+0x0+1x0 0x5+0x1+1x0) (0x0+0x0+0x0 0x1+0x0+0x0 0x5+0x1+0x0)] A^2 = [(0 0 1)(0 0 0)(0 0 0)] Sekarang kita hitung nilai A^3 A^3 = A x A x A A^3 = A^2 x A = [(0 0 1)(0 0 0)(0 0 0)] [(0 1 5)(0 0 1)(0 0 0)] A^3 = [(0x0+0x0+1x0 0x1+0x0+1x0 0x5+0x1+1x0) (0x0+0x0+0x0 0x1+0x0+0x0 0x5+0x1+0x0) (0x0+0x0+0x0 0x1+0x0+0x0 0x5+0x1+0x0)] A^3 = [(0 0 0)(0 0 0)(0 0 0)] Sekarang kita hitung nilai A^4 A^4 = A x A x A x A A^4 = A^3 x A A^4 = [(0 0 0)(0 0 0)(0 0 0)] x A A^4 = [(0 0 0)(0 0 0)(0 0 0)] Karena matriks A saat berpangkat 3 dan 4 sudah bernilai [(0 0 0)(0 0 0)(0 0 0)], maka A^5 dan seterusnya = [(0 0 0)(0 0 0)(0 0 0)] Jadi, jawabannya adalah A. [(0 0 0)(0 0 0)(0 0 0)] Semoga membantu ya :)