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**Unformatted text preview: **And hence determine the conditions on a, b, c such that the set is LI on any interval. I used the transpose of A since they have the same determinant. 13. Determine whether the set is LI or LD on 14. Find those k values for which the following vectors are LD. 15. Determine if the vector lies in span where and are in R 3 . 16. Let S be the subspace of spanned by the vectors . Determine a basis for S , and hence, find dim[ S ]. Thus Dim[S]=2 Basis is any 2 of the given vectors. 17. In question (a) compute the Wronskian (It is not equal to zero so they are LI) In question (b)if you compute the Wronskian it will be equal to zero and by quick inspection you can see they are LD. 18. Find the dimension of the null space of the matrix Det(A)is not equal to zero therefore Nullspace of A contains only the zero vector hence its dimension is zero. 19. Are the polynomials a basis for P 3 (the vector space of polynomials of degree at most three)? Justify your answer...

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