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Linear Algebra

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Linear Combination of Vectors

LINALG-WLSCEB

Can we express the vector $(1,1,1)$ as a linear combination of the vectors $(1, 0, 1), (1,2, 2), (0,1,1)$ and $(-1, 1, -2)$?

A

No, because $(1,1,1)$ is a vector in $R^3$ and so it should be expressed as a linear combination of three vectors not four.

B

No, because $(1,1,1)=1*(1,0,0)+1*(0,1,0)+1*(0,0,1)$.

C

Yes. $(1,1,1)=3(1,0,1)+(-1)(1,2,2)+2(0,1,1)+(1)(-1,1,2).$

D

Choice 'A' and Choice 'B' are both correct.