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 M22 given by L(A) = A- AT. Find a basis for ker(L).

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 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

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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Question

Linear algerba

6. (a) Let D : P → P 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 M22
given by
L(A) = A – AT.
Find a basis for ker(L).
We krow DLPEXI) = p'(x}.
la),
kerlD)
: { Pot a, so , az=0}
Cinfused about
notutóns aned
$ Poxy=
the solytion.
Same thing ?
the flrst one
Is domcnin ?
secand ane is codomin?

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