Fall-09-keytestrev2

# Fall-09-keytestrev2 - And hence determine the conditions on...

This preview shows pages 1–14. Sign up to view the full content.

Math 2090, Spring 2009. Name._____________ Testreview2 Section.______7_____ 1. Determine all values of the constant k for which the following system has an infinite number of solutions. 2. Reduce the given matrix to upper triangular form and then evaluate the determinant.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3. Use the cofactor expansion theorem to evaluate the determinant along column 3. 4. Use the adjoint method to find A -1 if
5. Use the Cramer’s rule to determine x 1 and x 2 6. Consider the vector space and let S be the subset of V consisting of those functions satisfying the DE on I . Determine whether S is a subspace of V .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
7. Let , and is he set of all vectors in V satisfying . Determine whether S is a subspace of V . 8. Determine the null space of the matrix
9. Determine whether the set is LI or LD in. In case of linear dependence, find a dependency relationship. 10. Find those x values for which the following vectors are LD

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
11. Determine whether the set is LI in. SO THEY ARE L.D. 12. Show that the following functions have Wronskian

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

### Page1 / 14

Fall-09-keytestrev2 - And hence determine the conditions on...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online