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Linear combination

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Suppose you have three vectors (1,0,1), (1,2,0), (0,1,-1) and three numbers 2, 1, 1/2. Then their linear combination is a new vector

2(1,0,1) + 1(1,2,0) + 1/2(0,1,-1)
= (2,0,2) + (1,2,0) + (0,1/2,-1/2)
= (2+1+0, 0+2+1/2, 2+0-1/2)
= (3, 2 1/2, 1 1/2).

Generalities are here: Linear algebra.