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Consider the vector space U of all skew-symmetric matrices in M3,3, i.e. all 3 × 3-matrices A such that A = -A". Which of the following vector spaces is U isomorphic to? In each case you either need to prove that U is not isomorphic to the corresponding vector space or construct an isomorphism from that vector space to U. • The space R². • The space P2 of all polynomials of degree < 2. • The space M2,2 of 2 × 2-matrices.

Consider the vector space U of all skew-symmetric matrices in M3,3, i.e. all 3 × 3-matrices A such that A = -A". Which of the following vector spaces is U isomorphic to? In each case you either need to prove that U is not isomorphic to the corresponding vector space or construct an isomorphism from that vector space to U. • The space R². • The space P2 of all polynomials of degree < 2. • The space M2,2 of 2 × 2-matrices.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the vector space U of all skew-symmetric matrices in M3.3, i.e. all 3 x 3-matrices A such that A = -AT. Which of the following vector spaces is U isomorphic to? In each case you either need to prove that U is not isomorphic to the corresponding vector space or construct an isomorphism from that vector space to U. • The space R². • The space P2 of all polynomials of degree < 2. • The space M2.2 of 2 × 2-matrices.
Transcribed Image Text:Consider the vector space U of all skew-symmetric matrices in M3.3, i.e. all 3 x 3-matrices A such that A = -AT. Which of the following vector spaces is U isomorphic to? In each case you either need to prove that U is not isomorphic to the corresponding vector space or construct an isomorphism from that vector space to U. • The space R². • The space P2 of all polynomials of degree < 2. • The space M2.2 of 2 × 2-matrices.
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