Q3. Let L: R2R2 be a mapping from the vector space R2 to itself defined by L(x , y)= ( 2x+y, x-3y) for each (x.y) belong to R?. Show that L is a linear operator on R² and then find the representation matrix ms(L), where S is the standard bases of R?.

Q3. Let L: R2R2 be a mapping from the vector space R2 to itself defined by L(x , y)= ( 2x+y, x-3y) for each (x.y) belong to R?. Show that L is a linear operator on R² and then find the representation matrix ms(L), where S is the standard bases of R?.

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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Concept explainers

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

Q3. Let L: R2-R2 be a mapping from the vector space R2 to itself
defined by L(x , y)= ( 2x+y, x-3y) for each (x,y) belong to R?. Show
that L is a linear operator on R² and then find the representation matrix
ms(L), where S is the standard bases of R2.

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