Unformatted text preview: 2. Determine whether each of the following are subspaces of P 3 1 (a) { p ∈ P 3 : p (1) = 0 } (b) { p ∈ P 3 : p (1) = 1 } (c) The set of all odd functions in P 3 3. Do the invertible 3 × 3 matrices form a subspace of M 3 × 3 ? 2 What about the matrices of the form a b c d e f ? Of the form a b c 1 d e 1 1 f ? 4. Consider the transformation T : P 3 → P 3 given by T ( p ) = p . Prove that T is a linear transformation and determine if it is 11 and if it is onto. 5. Let A be some ﬁxed 2 × 3 matrix. Prove that the set { B ∈ M 4 × 2 : AB = 0 } is a subspace of M 4 × 2 . 1 P n denotes the set of all polynomials with degree less than or equal to n 2 M m × n denotes the set of all m × n matrices...
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at Berkeley.
 Fall '10
 yildiz
 Math

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