Express the vector `hat(i) + 4hat(j) - 4hat(k)` as a linear combination of the vectors `2hat(i) - hat(j) + 3hat(k), hat(i) - 2hat(j) + 4hat(k)` and `-hat(i) + 3hat(j) - 5hat(k)`

Answer

`hat(i) + 4hat(j) - 4hat(k) = 1(2hat(i) - hat(j) + 3hat(k)) + 2(hat(i) - 2hat(j) + 4hat(k)) + 3(-hat(i) + 3hat(j) - 5hat(k))`