Diketahui vektor U (-1,4,2) dan vektor V = (3,-2,6) Tentukan vektor B yang memenuhi persamaan berikut a) 2U - 3V- W = vektor 0(nol) b) 5V-W-2U=U-3W Tolong diban

Kategori Soal : Matematika - Vektor
Kelas : XII (3 SMA)
Pembahasan : 
Diketahui vektor baris u = (-1, 4, 2) dan v = (3, -2, 6).
a. 2u - 3v - w = 0
⇔ w = 2u - 3v
⇔ w = 2(-1, 4, 2) - 3(3, -2, 6)
⇔ w = (-2, 8, 4) - (9, -6, 18)
⇔ w = (-2 - 9, 8 - (-6), 4 - 18)
⇔ w = (-11, 8 + 6, -14)
⇔ w = (-11, 14, -14)

b. 5v - w - 2u = u - 3w
⇔ -w + 3w = u + 2u - 5v
⇔ 2w = 3u - 5v
⇔ 2w = 3(-1, 4, 2) - 5(3, -2, 6)
⇔ 2w = (-3, 12, 6) - (15, -10, 30)
⇔ 2w = (-3 - 15, 12 - (-10), 6 - 30)
⇔ 2w = (-18, 12 + 10, -24)
⇔ 2w = (-18, 22, -24)
⇔ w = (-9, 11, -12)

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