1. Let C[a,b] denote the set of all real-valued continuous functions on [a,b]. If g and f are in C[a,b],we define fOg =f(t) +g(t) and c©f = c f(t) for all scalars c.a. Show that C[a,b] is a real vector space.b. Let Wk be the set of all functions in C[a,b] such that f(a) = k. For what values of k will Wk be%3Da subspace of C[a,b]?

1. Let C[a,b] denote the set of all real-valued continuous functions on [a,b]. If g and f are in C[a,b], we define fOg = f(t) +g(t) and c©f = c f(t) for all scalars c. Show that C[a,b] is a real vector space. а. b. Let Wk be the set of all functions in C[a,b] such that f(a) = k. For what values of k will Wk be %3D a subspace of C[a,b]?

1. Let C[a,b] denote the set of all real-valued continuous functions on [a,b]. If g and f are in C[a,b], we define fOg = f(t) +g(t) and c©f = c f(t) for all scalars c. Show that C[a,b] is a real vector space. а. b. Let Wk be the set of all functions in C[a,b] such that f(a) = k. For what values of k will Wk be %3D a subspace of C[a,b]?

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

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

1. Let C[a,b] denote the set of all real-valued continuous functions on [a,b]. If g and f are in C[a,b],
we define fOg =f(t) +g(t) and c©f = c f(t) for all scalars c.
a. Show that C[a,b] is a real vector space.
b. Let Wk be the set of all functions in C[a,b] such that f(a) = k. For what values of k will Wk be
%3D
a subspace of C[a,b]?

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