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P₁ be a linear transformation defined as a) Is 2+ Xe R(7) ? T((a, b, c)) = (a-2b) + (2b + c) X

P₁ be a linear transformation defined as a) Is 2+ Xe R(7) ? T((a, b, c)) = (a-2b) + (2b + c) X

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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Let T: IR→ P₁ be a linear transformation defined as a) Is 2 + X = R(7) ? b) Is (2, 1, -1) € Ker(7) ? c) Find a basis of Ker(7). T((a, b, c)) = (a-2b) + (2b+c) X d) Find the rank and the nullity of T. 7
Transcribed Image Text:Let T: IR→ P₁ be a linear transformation defined as a) Is 2 + X = R(7) ? b) Is (2, 1, -1) € Ker(7) ? c) Find a basis of Ker(7). T((a, b, c)) = (a-2b) + (2b+c) X d) Find the rank and the nullity of T. 7
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