(a) Let D: P3 → P3 be the differentiation operator. Find the kernel and range of D. (b) Let M22 be the vector space of 2 × 2 real matrices. Let L be the linear operator on M22 given by L(A) = A – AT. Find a basis for ker(L).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
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6. (a) Let D: P3 → P3 be the differentiation operator. Find the kernel and range of D.
(b) Let M2.2 be the vector space of 2 x 2 real matrices. Let L be the linear operator on M2,2
given by
L(A) = A – AT.
Find a basis for ker(L).
Transcribed Image Text:6. (a) Let D: P3 → P3 be the differentiation operator. Find the kernel and range of D. (b) Let M2.2 be the vector space of 2 x 2 real matrices. Let L be the linear operator on M2,2 given by L(A) = A – AT. Find a basis for ker(L).
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