QUESTION 3 Consider the vector space V = C² with scalar multiplication over the real numbers R, and let T:V→ V be the linear operator defined by T(Z₁, Z₂) = (Z₁-Z₁, iZ₁ + Z₂). (3.1) Find a basis for N (T). (3.2) Find a basis for R (T). (3.3) Show that V = N(T) +R(T). (3.4) Find a basis for V such that [7]B = [01x1 01x3] X 03x1 for some X € M3x3 (C).
QUESTION 3 Consider the vector space V = C² with scalar multiplication over the real numbers R, and let T:V→ V be the linear operator defined by T(Z₁, Z₂) = (Z₁-Z₁, iZ₁ + Z₂). (3.1) Find a basis for N (T). (3.2) Find a basis for R (T). (3.3) Show that V = N(T) +R(T). (3.4) Find a basis for V such that [7]B = [01x1 01x3] X 03x1 for some X € M3x3 (C).
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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