## Linear Combination

The program determines the linear combination of a vector from three given vectors. An error message is displayed if these vectors are linearly dependent.

You can use this routine to prove the linear independence of three vectors, i.e. to prove if they lie in one plane.

### Example 1:

⎧ 1 ⎫ ⎧ 1 ⎫ ⎧ 1 ⎫ ⎧ 2 ⎫ a·⎪ 0 ⎪ + b·⎪ 1 ⎪ + c·⎪ 1 ⎪ = ⎪ 3 ⎪ ⎩ 0 ⎭ ⎩ 0 ⎭ ⎩ 1 ⎭ ⎩ 4 ⎭ Solution: a = -1 b = -1 c = 4

### Example 2:

⎧ 1 ⎫ ⎧ 2 ⎫ ⎧ 1 ⎫ ⎧ 2 ⎫ a·⎪ 2 ⎪ + b·⎪ 1 ⎪ + c·⎪ 5 ⎪ = ⎪ 3 ⎪ ⎩ 0 ⎭ ⎩ 1 ⎭ ⎩-1 ⎭ ⎩ 7 ⎭ The vectors are linearly dependent