Let M2x2 be the vector space of all 2 x 2 matrices, and define T: M2x2 - R by T(A) = tr(A) where A = ( ) and Tr(A) is trace of A. Note that trace of a square matrix is sum of all element on its main diagonal, Tr(A) = a + d. a) Show that T is a linear tranformation; b) Describe the kemel of T, write out one basis of Ker(T).

Let M2x2 be the vector space of all 2 x 2 matrices, and define T: M2x2 - R by T(A) = tr(A) where A = ( ) and Tr(A) is trace of A. Note that trace of a square matrix is sum of all element on its main diagonal, Tr(A) = a + d. a) Show that T is a linear tranformation; b) Describe the kemel of T, write out one basis of Ker(T).

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Let Max2 be the vector space of all 2 x 2 matrices, and define
T:Max2 → R by T(A) = tr(4)
where A = ( ) and Tr(A) is trace of A. Note that trace of a square matrix is sum of all
element on its main diagonal, Tr(A) = a + d.
a) Show that T is a linear tranformation;
b) Describe the kemel of T, write out one basis of Ker(T).

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