Diketahui matriks S = ((2,,0)(−1,,3)) dan M = ((1,,2)(0,,−3)). Jika fungsi f(S,M) = S² − M², maka matriks f(S+M, S−M) adalah ...

Jawaban yang benar adalah f(S+M, S−M) = ((4 20)(4 -40)). Ingat! Penjumlahan dua buah matriks: A+B = [(a b)(c d)] + [(e f)(g h)] = [(a+e b+f)(c+g d+h)] Perkalian dua buah matriks: AB = [(a b)(c d)] [(e f)(g h)] = [(ae+bg af+bh)(ce+dg cf+dh)] Perkalian matriks dengan skalar: kA = k[(a b)(c d)] = [(ka kb)(kc kd)] Sifat distributif pada perkalian matriks : A(B+C) = AB+AC Diketahui matriks S = ((2 0)(−1 3)) dan M = ((1 2)(0 −3)). Diketahui fungsi f(S,M) = S² − M² Sehingga f(S+M, S−M) = (S+M)² - (S-M)² = (S+M)(S+M) - (S-M)(S-M) = S(S+M) + M(S+M) - S(S-M) + M(S-M) = SS- SS + SM+SM + MS+ MS + MM-MM = 2SM + 2MS 2SM = 2 × ((2 0)(−1 3)) × ((1 2)(0 −3)) = ((4 0)(−2 6)) × ((1 2)(0 −3)) = ((4•1+0•0 4•2+0•(-3))(-2•1+6•0 (-2)•2+6•(-3)) = ((4+0 8+0)(-2+0 -4-18)) = ((4 8)(-2 -22)) 2MS = 2 × ((1 2)(0 −3)) × ((2 0)(−1 3)) = ((2 4)(0 −6)) × ((2 0)(−1 3)) = ((2•2+4•(-1) 2•0+4•3)(0•2+(-6)•(-1) 0•0+(-6)•3)) = ((4-4 0+12)(0+6 0-18)) = ((0 12)(6 -18)) Sehingga f(S+M, S−M) = 2SM + 2MS = ((4 8)(-2 -22)) + ((0 12)(6 -18)) = ((4+0 8+12)(-2+6 -22+(-18)) = ((4 20)(4 -40)) Jadi, f(S+M, S−M) = ((4 20)(4 -40)).