math 235 ch 4 practice

# math 235 ch 4 practice - T is an isomor-phism. 4. Let T : P...

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Math 235 - Section 6, Chapter 4 Practice Problems Adam Gamzon 1. Is the subset of upper triangular 3 × 3 matrices a subspace of R 3 × 3 ? 2. Is the set { f ( x ) in P 2 : f 00 ( x ) - 2 f ( x ) = 0 } a subspace of P 2 ? 3. Let T : R 2 × 2 R 2 × 2 be a linear transformation deﬁned by T ( M ) = ± 1 2 3 6 ² M . (a) Find the matrix of T with respect to the basis ± 1 1 0 0 ² , ± 1 0 1 0 ² , ± 1 0 0 1 ² , ± 0 1 1 0 ² . (b) Compute the determinant of the matrix found in part (a) to determine if
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Unformatted text preview: T is an isomor-phism. 4. Let T : P 3 P 3 be a linear transformation dened by T ( f ( x )) = f ( x ). (a) Find ker T . (b) Does the equation T ( f ( x )) = 2 x have a unique solution? Find all solutions f ( x ) in P 2 to this equation. 1...
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## This note was uploaded on 11/22/2011 for the course MATH 255 taught by Professor Staff during the Spring '10 term at UMass (Amherst).

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