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Let V be an inner product space and let W be a fixed veclor in V. Let L: V -+ R be

Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill ISBN: 9780132296540 301

Solution for problem 18 Chapter 6.1

Elementary Linear Algebra with Applications | 9th Edition

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Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill

Elementary Linear Algebra with Applications | 9th Edition

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Problem 18

Let V be an inner product space and let W be a fixed veclor in V. Let L: V -+ R be defined by L (v) = (, .. w) for V in V. Show that L is a linear transfonnation.

Step-by-Step Solution:
Step 1 of 3

Math246 Lecture 3: Separable Equations This is our first look at non­linear first order differential equations. Separable equations take the dy form P (y)dx=W (x) . Solving these equations is fairly straightforward. We will take a 3 step approach. 1. Rewrite into the form P(y)dy=W (x)dx 2. Integrate both sides: P y dy= W(x)dx ∫ ( ) ∫ 3. Solve for the general or explicit solution. There’s not much left to say except let’s work through a few examples, so let’s work through a few examples! Examples dy 3 1. Solve =7x y dx Ok, first we move everything into place. 1 3 dy=7x dx y Next, we integrate both sides. 1 3 ∫ dy=∫7x dx y 3 7 x . The integral of 1/y is the natural log function and the integra is 4 . l|y|= 7 x +C 4 y And now we solve for by taking the exponential of both sides. 7 4x y=Ae eC Where A is the constant Let’s work through one with a condition. 2x −x−1 f(x)= 3 y(1)=15 2. 2y −6 , Ok, first we rewrite it into a proper form. 2 x (¿¿4−x−1)dx 3 (2y −6)dy=¿ And now we

Step 2 of 3

Chapter 6.1, Problem 18 is Solved
Step 3 of 3

Textbook: Elementary Linear Algebra with Applications
Edition: 9
Author: Bernard Kolman David Hill
ISBN: 9780132296540

This textbook survival guide was created for the textbook: Elementary Linear Algebra with Applications, edition: 9. The full step-by-step solution to problem: 18 from chapter: 6.1 was answered by , our top Math solution expert on 01/30/18, 04:18PM. The answer to “Let V be an inner product space and let W be a fixed veclor in V. Let L: V -+ R be defined by L (v) = (, .. w) for V in V. Show that L is a linear transfonnation.” is broken down into a number of easy to follow steps, and 41 words. Since the solution to 18 from 6.1 chapter was answered, more than 228 students have viewed the full step-by-step answer. Elementary Linear Algebra with Applications was written by and is associated to the ISBN: 9780132296540. This full solution covers the following key subjects: . This expansive textbook survival guide covers 57 chapters, and 1519 solutions.

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Let V be an inner product space and let W be a fixed veclor in V. Let L: V -+ R be