testrev2

testrev2 - relationship 10 Find those x values for which...

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Math 2090, Fall 2009. Testreview2 Review Sections: 3.1-3.4 and 4.1 -4.6 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. 3. Use the cofactor expansion theorem to evaluate the determinant along column 3. 4. Use the adjoint method to find A -1 if
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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 . 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
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9. Determine whether the set is LI or LD in. In case of linear dependence, find a dependency
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Unformatted text preview: relationship. 10. Find those x values for which the following vectors are LD 11. Determine whether the set is LI in. 12. Show that the following functions have Wronskian And hence determine the conditions on a, b, c such that the set is LI on any interval. 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 ]. 17. 18. Find the dimension of the null space of the matrix 19. Are the polynomials a basis for P 3 (the vector space of polynomials of degree at most two)? Justify your answer...
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testrev2 - relationship 10 Find those x values for which...

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