Suppose vector{x(a + 3b + 4c) + y(a - 2b + 3c) + z(a + 5b - 2c) = 6a + 14b + 4c}
=> (x + y + z)a + (3x – 2y + 5z)b + (4x + 3y – 2z)c = 6a + 14b + 4c
=> x + y + z = 6 (1)
=> 3x – 2y + 5z = 14 (2)
=> 4x + 3y – 2z = 4 (3)
2(1) + (2) => 5x + 7z = 26 => (4)
3(1) – (3) => –x + 5z = 14 => (5)
5(5) + (4) => 32z = 96 => z = 3
(4) => 5x + 7(3) = 26 => 5x = 5 => x = 1; (1)
=> 1 + y + 3 = 6 => y = 2
vector{1(a + 3b + 4c) + 2(a - 2b + 3c) + 3(a + 5b - 2c) - 1(6a + 14b + 4c) = 0}