tolong jawab soal matriks pada soal ​pake cara ya

Jawaban: cara menghitung setiap operasi matriks pada soal nomor 2. Soal 2: Matriks A = [[2, 3, -1], [0, 2, 5], [1, 4, 3]]a. A² (A kuadrat):A² = A * A, yang berarti kita mengalikan matriks A dengan dirinya sendiri.- Langkah 1: Hitung Elemen-elemen A²A² = [[2, 3, -1], [0, 2, 5], [1, 4, 3]] * [[2, 3, -1], [0, 2, 5], [1, 4, 3]]- Elemen (1,1) A² = (2*2) + (3*0) + (-1*1) = 4 + 0 - 1 = 3- Elemen (1,2) A² = (2*3) + (3*2) + (-1*4) = 6 + 6 - 4 = 8- Elemen (1,3) A² = (2*-1) + (3*5) + (-1*3) = -2 + 15 - 3 = 10- Elemen (2,1) A² = (0*2) + (2*0) + (5*1) = 0 + 0 + 5 = 5- Elemen (2,2) A² = (0*3) + (2*2) + (5*4) = 0 + 4 + 20 = 24- Elemen (2,3) A² = (0*-1) + (2*5) + (5*3) = 0 + 10 + 15 = 25- Elemen (3,1) A² = (1*2) + (4*0) + (3*1) = 2 + 0 + 3 = 5- Elemen (3,2) A² = (1*3) + (4*2) + (3*4) = 3 + 8 + 12 = 23- Elemen (3,3) A² = (1*-1) + (4*5) + (3*3) = -1 + 20 + 9 = 28Jadi, A² = [[3, 8, 10], [5, 24, 25], [5, 23, 28]]b. Aᵀ.A (A Transpose dikalikan A): @Ara1412- Langkah 1: Cari Transpose Matriks A (Aᵀ)Transpose matriks diperoleh dengan mengubah baris menjadi kolom.Aᵀ = [[2, 0, 1], [3, 2, 4], [-1, 5, 3]]- Langkah 2: Perkalian Matriks Aᵀ dengan AAᵀ.A = [[2, 0, 1], [3, 2, 4], [-1, 5, 3]] * [[2, 3, -1], [0, 2, 5], [1, 4, 3]]- Elemen (1,1) Aᵀ.A = (2*2) + (0*0) + (1*1) = 4 + 0 + 1 = 5- Elemen (1,2) Aᵀ.A = (2*3) + (0*2) + (1*4) = 6 + 0 + 4 = 10- Elemen (1,3) Aᵀ.A = (2*-1) + (0*5) + (1*3) = -2 + 0 + 3 = 1- Elemen (2,1) Aᵀ.A = (3*2) + (2*0) + (4*1) = 6 + 0 + 4 = 10- Elemen (2,2) Aᵀ.A = (3*3) + (2*2) + (4*4) = 9 + 4 + 16 = 29- Elemen (2,3) Aᵀ.A = (3*-1) + (2*5) + (4*3) = -3 + 10 + 12 = 19- Elemen (3,1) Aᵀ.A = (-1*2) + (5*0) + (3*1) = -2 + 0 + 3 = 1- Elemen (3,2) Aᵀ.A = (-1*3) + (5*2) + (3*4) = -3 + 10 + 12 = 19- Elemen (3,3) Aᵀ.A = (-1*-1) + (5*5) + (3*3) = 1 + 25 + 9 = 35Jadi, Aᵀ.A = [[5, 10, 1], [10, 29, 19], [1, 19, 35]]c. A.Aᵀ (A dikalikan A Transpose):- Kita sudah punya A dan Aᵀ. Sekarang kalikan A dengan Aᵀ.A.Aᵀ = [[2, 3, -1], [0, 2, 5], [1, 4, 3]] * [[2, 0, 1], [3, 2, 4], [-1, 5, 3]]- Elemen (1,1) A.Aᵀ = (2*2) + (3*3) + (-1*-1) = 4 + 9 + 1 = 14- Elemen (1,2) A.Aᵀ = (2*0) + (3*2) + (-1*5) = 0 + 6 - 5 = 1- Elemen (1,3) A.Aᵀ = (2*1) + (3*4) + (-1*3) = 2 + 12 - 3 = 11- Elemen (2,1) A.Aᵀ = (0*2) + (2*3) + (5*-1) = 0 + 6 - 5 = 1- Elemen (2,2) A.Aᵀ = (0*0) + (2*2) + (5*5) = 0 + 4 + 25 = 29- Elemen (2,3) A.Aᵀ = (0*1) + (2*4) + (5*3) = 0 + 8 + 15 = 23- Elemen (3,1) A.Aᵀ = (1*2) + (4*3) + (3*-1) = 2 + 12 - 3 = 11- Elemen (3,2) A.Aᵀ = (1*0) + (4*2) + (3*5) = 0 + 8 + 15 = 23- Elemen (3,3) A.Aᵀ = (1*1) + (4*4) + (3*3) = 1 + 16 + 9 = 26 Jadi, A.Aᵀ = [[14, 1, 11], [1, 29, 23], [11, 23, 26]] d. (Aᵀ)² (A Transpose dikuadratkan): (Aᵀ)² = Aᵀ * Aᵀ, yang berarti kita mengalikan transpose matriks A dengan dirinya sendiri.- Aᵀ = [[2, 0, 1], [3, 2, 4], [-1, 5, 3]]- (Aᵀ)² = [[2, 0, 1], [3, 2, 4], [-1, 5, 3]] * [[2, 0, 1], [3, 2, 4], [-1, 5, 3]]- Elemen (1,1) (Aᵀ)² = (2*2) + (0*3) + (1*-1) = 4 + 0 - 1 = 3- Elemen (1,2) (Aᵀ)² = (2*0) + (0*2) + (1*5) = 0 + 0 + 5 = 5- Elemen (1,3) (Aᵀ)² = (2*1) + (0*4) + (1*3) = 2 + 0 + 3 = 5- Elemen (2,1) (Aᵀ)² = (3*2) + (2*3) + (4*-1) = 6 + 6 - 4 = 8- Elemen (2,2) (Aᵀ)² = (3*0) + (2*2) + (4*5) = 0 + 4 + 20 = 24- Elemen (2,3) (Aᵀ)² = (3*1) + (2*4) + (4*3) = 3 + 8 + 12 = 23- Elemen (3,1) (Aᵀ)² = (-1*2) + (5*3) + (3*-1) = -2 + 15 - 3 = 10- Elemen (3,2) (Aᵀ)² = (-1*0) + (5*2) + (3*5) = 0 + 10 + 15 = 25- Elemen (3,3) (Aᵀ)² = (-1*1) + (5*4) + (3*3) = -1 + 20 + 9 = 28Jadi, (Aᵀ)² = [[3, 5, 5], [8, 24, 23], [10, 25, 28]]Ringkasan Hasil:- A² = [[3, 8, 10], [5, 24, 25], [5, 23, 28]]- Aᵀ.A = [[5, 10, 1], [10, 29, 19], [1, 19, 35]]- A.Aᵀ = [[14, 1, 11], [1, 29, 23], [11, 23, 26]]- (Aᵀ)² = [[3, 5, 5], [8, 24, 23], [10, 25, 28]]Penjelasan dengan langkah-langkah:maaf cuman bisa bantu segitu,kolom jawabnya tidak muat,penuh

Answered by ara1412 | 2025-08-12