Find a basis for thesubspace of R 3 spanned by S = {(-1, 2, 5), (3, 0, 3), (5, 1

Question

Find a basis for thesubspace of R3 spanned by S = {(-1, 2, 5), (3, 0, 3), (5, 1, 8)}            v1             v2          v3 The author of my textbook use the vectors in S to formthe rows of a matrix, and rewrite this matrix in row-ecelonform. The nonzero matix will then form a basis for the subspacespanned by S. But, If I know that the set S is linearly dependent, canI simply take one of the vectors, sayv3  ,out. And say the remainig twovectors,v1 and v2 , forma  basis for the subspace spanned by S. Find a basis for thesubspace of R3 spanned by S = {(-1, 2, 5), (3, 0, 3), (5, 1, 8)}            v1             v2          v3 The author of my textbook use the vectors in S to formthe rows of a matrix, and rewrite this matrix in row-ecelonform. The nonzero matix will then form a basis for the subspacespanned by S. But, If I know that the set S is linearly dependent, canI simply take one of the vectors, sayv3  ,out. And say the remainig twovectors,v1 and v2 , forma  basis for the subspace spanned by S. The author of my textbook use the vectors in S to formthe rows of a matrix, and rewrite this matrix in row-ecelonform. The nonzero matix will then form a basis for the subspacespanned by S. But, If I know that the set S is linearly dependent, canI simply take one of the vectors, sayv3  ,out. And say the remainig twovectors,v1 and v2 , forma  basis for the subspace spanned by S.

Explanation / Answer

you can prove that
v3=(1/2)v1+(11/6)v2
So v1 and v2 form a basis for the whole subset

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