1. Let W be a vector space of all symmetric 2 x 2 matrices. Let T : W → P2(R) be a linear transformation defined by ) = (a – 6) + (& – c)r + (c – – a)x². T Find the nullity and rank of T. Is T an isomorphism? Why?
1. Let W be a vector space of all symmetric 2 x 2 matrices. Let T : W → P2(R) be a linear transformation defined by ) = (a – 6) + (& – c)r + (c – – a)x². T Find the nullity and rank of T. Is T an isomorphism? Why?
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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Transcribed Image Text:1. Let W be a vector space of all symmetric 2 x 2 matrices. Let T: W → P2(R)
be a linear transformation defined by
T
6 c
b7
— (а — b) + (b — с)т + (с — а)1*.
Find the nullity and rank of T. Is T an isomorphism? Why?
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