Linear Algebra with Applications (3rd Edition)

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110.201 Linear Algebra 3rd Quiz March 24, 2005 Notation. P n = space of polynomials, with real coefficients, of degree at most n . R m × n = space of m by n real matrices. Problem 1 Determine whether the following spaces are isomorphic. In case they are isomorphic, define an isomorphism relating them. Justify your answer. 1. R 2 and R 4 2. P 5 and R 5 3. R 2 × 3 and R 6 4. P 5 and R 2 × 3 5. R 2 × k and C k , for k N Problem 2 Let V = C 1 ([0 , 1]) be the set of continuously differentiable func- tions on the closed interval [0 , 1]. V is a real linear space with respect to the operations of pointwise addition of functions and scalar multiplication.
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