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(b) Let T: R³ →R³, T(v) = (v₂w;)w; +(v, w,₂)w, where w, = (1,-1,0) and w₂ = (0,2,1). (1) Find the kernel of T. (ii) Find the range of T. (iii) Find the nullity and rank. (iv) Determine whether T is one-to-one and onto. Justify your answer. (v) Is it an isomorphism? Justify your answer.

(b) Let T: R³ →R³, T(v) = (v₂w;)w; +(v, w,₂)w, where w, = (1,-1,0) and w₂ = (0,2,1). (1) Find the kernel of T. (ii) Find the range of T. (iii) Find the nullity and rank. (iv) Determine whether T is one-to-one and onto. Justify your answer. (v) Is it an isomorphism? Justify your answer.

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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(b) Let T: R³ R³, T(v) = (v. w;)w; +(v,w₂)w, where w; = (1,-1,0) and w₂ = (0,-2,1). (1) Find the kernel of 7. (ii) Find the range of T. (iii) Find the nullity and rank. (iv) Determine whether T is one-to-one and onto. Justify your answer. (v) Is it an isomorphism? Justify your answer.
Transcribed Image Text:(b) Let T: R³ R³, T(v) = (v. w;)w; +(v,w₂)w, where w; = (1,-1,0) and w₂ = (0,-2,1). (1) Find the kernel of 7. (ii) Find the range of T. (iii) Find the nullity and rank. (iv) Determine whether T is one-to-one and onto. Justify your answer. (v) Is it an isomorphism? Justify your answer.
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