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The problem is attached.

I don't know why he called all 4 vectors V1, I guess it was a typo.

Anyways, part I) This is not linearly independent as the determinant of the matrix containing those 4 vectors is 0

I am having trouble with part II)

I think I know the answer, but I don't think my explanation is right.

I said you can find a subset of vectors that are linearly independent, BUT not have the same span. The span of the original four vectors is c1v1+c2v2+c3v3+c4v4, where c1,c2,c3, c4 are real #s. The subset is independent, thus, the vectors cannot be written as a linear combination, thus, it doesn't have a span?

I don't know why he called all 4 vectors V1, I guess it was a typo.

Anyways, part I) This is not linearly independent as the determinant of the matrix containing those 4 vectors is 0

I am having trouble with part II)

I think I know the answer, but I don't think my explanation is right.

I said you can find a subset of vectors that are linearly independent, BUT not have the same span. The span of the original four vectors is c1v1+c2v2+c3v3+c4v4, where c1,c2,c3, c4 are real #s. The subset is independent, thus, the vectors cannot be written as a linear combination, thus, it doesn't have a span?