Let L be a linear operaton on a vector space V. Let A =with respect to a basis B =[LR be the matrix representing LB{V1,..., Vn} of V. Show that Am is the matrix representing Lmwith respect to B; that is, show that [L"]g= ([L]s)™m

Let, L be linear operator on the vector space V. Let, A be the matrix representing L with respect to…

Let L be a linear operaton on a vector space V. Let A = vith respect to a basis B = {v1,., Vn} of V. Show that Am is the matrix representing Lm LR be the matrix representing L vith respect to B; that is, show that [Lml = ([L],)".

Let L be a linear operaton on a vector space V. Let A = vith respect to a basis B = {v1,., Vn} of V. Show that Am is the matrix representing Lm LR be the matrix representing L vith respect to B; that is, show that [Lml = ([L],)".

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let L be a linear operaton on a vector space V. Let A =
with respect to a basis B =
[LR be the matrix representing L
B
{V1,..., Vn} of V. Show that Am is the matrix representing Lm
with respect to B; that is, show that [L"]g= ([L]s)™
m

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