Jika diberikan matriks-matriks berikut. A=(5 1 2 0 7 -4 3

Matriks hasil perhitungan adalah [[-28, -10, 28], [-12, 36, -32], [-6, -10, 8]].

Pembahasan

Diberikan matriks-matriks:
A = [5 1 2; 0 7 -4; 3 -2 5]
B = [7 2 -4; 2 -3 4; 2 1 1]

Kita perlu menghitung 2(A - 3B) + 4I, di mana I adalah matriks identitas.

Langkah 1: Hitung 3B
3B = 3 * [7 2 -4; 2 -3 4; 2 1 1]
3B = [21 6 -12; 6 -9 12; 6 3 3]

Langkah 2: Hitung A - 3B
A - 3B = [5 1 2; 0 7 -4; 3 -2 5] - [21 6 -12; 6 -9 12; 6 3 3]
A - 3B = [(5-21) (1-6) (2-(-12)); (0-6) (7-(-9)) (-4-12); (3-6) (-2-3) (5-3)]
A - 3B = [-16 -5 14; -6 16 -16; -3 -5 2]

Langkah 3: Hitung 2(A - 3B)
2(A - 3B) = 2 * [-16 -5 14; -6 16 -16; -3 -5 2]
2(A - 3B) = [-32 -10 28; -12 32 -32; -6 -10 4]

Langkah 4: Hitung 4I (matriks identitas 3x3 dikalikan 4)
4I = 4 * [1 0 0; 0 1 0; 0 0 1]
4I = [4 0 0; 0 4 0; 0 0 4]

Langkah 5: Hitung 2(A - 3B) + 4I
2(A - 3B) + 4I = [-32 -10 28; -12 32 -32; -6 -10 4] + [4 0 0; 0 4 0; 0 0 4]
2(A - 3B) + 4I = [(-32+4) (-10+0) (28+0); (-12+0) (32+4) (-32+0); (-6+0) (-10+0) (4+4)]
2(A - 3B) + 4I = [-28 -10 28; -12 36 -32; -6 -10 8]

Hasil akhirnya adalah matriks:
[-28 -10 28]
[-12 36 -32]
[-6 -10 8]