## Linear Combination

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

With this routine you may proof the linear independence of three vectors what means to proof if they are situated in a 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