Consider the vector space V = C² with scalar multiplication over the real numbers R (note that V is a vector space of dimension 4 over R). Let T: V→ V be the linear operator defined by T(Z₁, Z2)= (Z₁-Z₁, iZ₁ + Z₂). Use the Diagonalisability Test to explain whether T is diagonalisable over R. If T is diagonalisable, find a basis for V such that [7] is a diagonal matrix and write down [7]a- α
Consider the vector space V = C² with scalar multiplication over the real numbers R (note that V is a vector space of dimension 4 over R). Let T: V→ V be the linear operator defined by T(Z₁, Z2)= (Z₁-Z₁, iZ₁ + Z₂). Use the Diagonalisability Test to explain whether T is diagonalisable over R. If T is diagonalisable, find a basis for V such that [7] is a diagonal matrix and write down [7]a- α
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 10CM
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![QUESTION 4
Consider the vector space V = C² with scalar multiplication over the real numbers R (note that
V is a vector space of dimension 4 over R). Let TV → V be the linear operator defined by
T(Z₁, Z2) = (Z₁ Z₁, iZ₁ + Z₂). Use the Diagonalisability Test to explain whether T is diagonalisable
over R. If T is diagonalisable, find a basis a for V such that [7] is a diagonal matrix and write
down [T]-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabdd1821-d7b6-4171-a67e-edf70418727b%2F0430e4f1-d058-4661-be60-abf01a01d625%2Fg8t5cbj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 4
Consider the vector space V = C² with scalar multiplication over the real numbers R (note that
V is a vector space of dimension 4 over R). Let TV → V be the linear operator defined by
T(Z₁, Z2) = (Z₁ Z₁, iZ₁ + Z₂). Use the Diagonalisability Test to explain whether T is diagonalisable
over R. If T is diagonalisable, find a basis a for V such that [7] is a diagonal matrix and write
down [T]-
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