Diketahui vektor d=(2 1), e=(-4 2), dan f=(0 5). Carilah

Vektor c ditemukan untuk setiap persamaan: (6 -1), (2 2), (8 21), (-2 -10.5), dan (2 -4/7).

Pembahasan

1) d - x = e  => x = d - e = (2 1) - (-4 2) = (2 - (-4)  1 - 2) = (6 -1)
2) d + e + x = f => x = f - d - e = (0 5) - (2 1) - (-4 2) = (0 - 2 - (-4)  5 - 1 - 2) = (2 2)
3) 2e + x = 5f => x = 5f - 2e = 5(0 5) - 2(-4 2) = (0 25) - (-8 4) = (0 - (-8)  25 - 4) = (8 21)
4) -4d - 2x = e + 3f => -2x = e + 3f + 4d = (-4 2) + 3(0 5) + 4(2 1) = (-4 2) + (0 15) + (8 4) = (-4 + 0 + 8  2 + 15 + 4) = (4 21) => x = -1/2 (4 21) = (-2 -10.5)
5) 1/5f = d - 2/3e - 7/3x => 7/3x = d - 2/3e - 1/5f = (2 1) - 2/3(-4 2) - 1/5(0 5) = (2 1) - (-8/3 4/3) - (0 1) = (2 - (-8/3) - 0  1 - 4/3 - 1) = (2 + 8/3  -4/3) = (14/3 -4/3) => x = 3/7 (14/3 -4/3) = (2 -4/7)