question on The coefficients of vectors in a basis I understand that in a basis,

Q: question on The coefficients of vectors in a basis I understand that in a basis,

No it doesnt v1 = 1*v1 +0.v2+0*v3+..0*vn => v1 is written as a linear combination of {v1,v2,...,vn} but v1 cant be written as a linear combination of {v2,v3,...vn}

ID: 2965596 • Letter: Q

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question on The coefficients of vectors in a basis

I understand that in a basis, all the vectors are linearly independent. This should mean that none of the vectors can be expressed as a linear combination of the vectors preceding it. However, the definition of the coordinates of a vector say that if a set {v1...vn} form a basis of a vector space, then every vector v in the set can be written uniquely as a linear combination of the other vectors, with the coefficients being the coordinate vector of v. Doesn't this definition contradict the definition of linear independence?

Explanation / Answer

No it doesnt

v1 = 1*v1 +0.v2+0*v3+..0*vn

v1 is written as a linear combination of {v1,v2,...,vn}

but

v1 cant be written as a linear combination of {v2,v3,...vn}

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