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# midterm2 - Exam 2 Linear Algebra Dave Bayer Name ID[1(6...

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Exam 2 Linear Algebra, Dave Bayer, November 11, 1999 Name: ID: School: [ 1 ] (6 pts) [ 2 ] (6 pts) [ 3 ] (6 pts) [ 4 ] (6 pts) [ 5 ] (6 pts) TOTAL Please work only one problem per page, starting with the pages provided, and number all continuations clearly. Only work which can be found in this way will be graded. Please do not use calculators or decimal notation. [1] Let P be the set of all degree 4 polynomials in one variable x with real coeﬃcients. Let Q be the subset of P consisting of all odd polynomials, i.e. all polynomials f ( x )so f ( x )= f ( x ). Show that Q is a subspace of P . Choose a basis for Q . Extend this basis for Q to a basis for P . Page 1 Continued on page:

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Problem: Page 2 Continued on page:
[2] Let A be the matrix A = 0111 1111 1112 . Compute the row space and column space of A . Page 3 Continued on page:

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Problem: Page 4 Continued on page:
[3] Let L be the linear transformation from R 3 to R 3

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midterm2 - Exam 2 Linear Algebra Dave Bayer Name ID[1(6...

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