Diketahui Matriks A=(2 1 3 2), B=(5 1 4 2), dan C=(1 -2 0

-34

Pembahasan

Diketahui matriks A = [
[2, 1],
[3, 2]
], B = [
[5, 1],
[4, 2]
], dan C = [
[1, -2],
[0, 4]
].
Kita perlu mencari matriks P = 2A + B - C.

Langkah 1: Hitung 2A
2A = 2 * [
[2, 1],
[3, 2]
] = [
[4, 2],
[6, 4]
]

Langkah 2: Hitung 2A + B
2A + B = [
[4, 2],
[6, 4]
] + [
[5, 1],
[4, 2]
] = [
[4+5, 2+1],
[6+4, 4+2]
] = [
[9, 3],
[10, 6]
]

Langkah 3: Hitung P = (2A + B) - C
P = [
[9, 3],
[10, 6]
] - [
[1, -2],
[0, 4]
] = [
[9-1, 3-(-2)],
[10-0, 6-4]
] = [
[8, 5],
[10, 2]
]

Langkah 4: Hitung Determinan P
Determinan P = det(P) = (8 * 2) - (5 * 10)
Determinan P = 16 - 50
Determinan P = -34