Jika a={3 2 1], b=[1 2 3]; dan C=[0 1 2]. Tentukan a.

a. {5, 5, 5}, b. {0.5, 8, 15.5}

Pembahasan

Diberikan vektor a={3, 2, 1}, b=[1, 2, 3], dan c=[0, 1, 2].

a. Menghitung 2A - B + 3C:
2A = 2 * {3, 2, 1} = {6, 4, 2}
3C = 3 * {0, 1, 2} = {0, 3, 6}
2A - B + 3C = {6, 4, 2} - {1, 2, 3} + {0, 3, 6}
= {(6-1+0), (4-2+3), (2-3+6)}
= {5, 5, 5}

b. Menghitung (1/2B - A) + 3(B + C):
(1/2)B = (1/2) * {1, 2, 3} = {0.5, 1, 1.5}
(1/2)B - A = {0.5, 1, 1.5} - {3, 2, 1}
= {(0.5-3), (1-2), (1.5-1)}
= {-2.5, -1, 0.5}
B + C = {1, 2, 3} + {0, 1, 2}
= {(1+0), (2+1), (3+2)}
= {1, 3, 5}
3(B + C) = 3 * {1, 3, 5} = {3, 9, 15}
(1/2)B - A + 3(B + C) = {-2.5, -1, 0.5} + {3, 9, 15}
= {(-2.5+3), (-1+9), (0.5+15)}
= {0.5, 8, 15.5}