×
Log in to StudySoup
Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 3 - Problem 3.2.27
Join StudySoup for FREE
Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 3 - Problem 3.2.27

Already have an account? Login here
×
Reset your password

Find conditions on a, b, c, and d such that commutes with every 2 2 matrix

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 3.2.27 Chapter 3

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

4 5 1 347 Reviews
21
2
Problem 3.2.27

Find conditions on a, b, c, and d such that commutes with every 2 2 matrix.

Step-by-Step Solution:
Step 1 of 3

Product Rule If F(x)=f(x)g(x), Then F’(x)=f(x)g’(x) + f’(x)g(x) Ex. d/dx [ (4x^3 - x^2 -1)(x^3 -2x^2 + 3x +1)] = (4x^3 - X^2 - 1) (3x^2- 4x + 3) = (12x^2 -2x)(x^3 - 2x^2 + 3x + 1) However the product rule is more useful for the product of different types of functions Ex. f(x)= x^2cos(x) g(x) = e^x arctan(x) Proof of the Product Rule Let F(x) = f(x)g(x) F’(x) = lim ((F(x + h ) - F(x))/h) h 0 =lim ((f(x + h )g( x + h) - f(x)g(x))/h) h 0 Subtract and add f(x + h)g(x) = lim ((f( x + h)g(x + h) - f(x + h)g(x) + f(x + h) - g(x) - f(x)g(x))/h) h 0 = lim ((f( x + h)(g( x + h) - g(x)) + g(x)(f( x + h) - f(x))/h) h 0 = lim ((f ( x+ h)(g( x + h) - g(x))/h) + (g(x)f(x + h) - f(x)/h) h 0 = lim (f( x + h) lim ((g(x + h) - g(x))/h) + lim (g(x))lim((f(x + h) - f(x))/h) h 0 h 0 h 0 h 0 = f(x)g’(x) + g(x)f’(x) The Quotient Rule d/dx (f(x)/g(x)) = g(x)d/dx f(x) - f(x)d/dx (g(x))/(g(x))^2 If F(x) = f(x)/g(​ ’(x) = (g(x)f’(x) - f(x)g’(x))/(g(x)^2) Rhyme for remembering quotient rule “ Low times d-high minus high. D-low, over the square of what’s below” Ex. d/dx [x/x^2-1] = ((x^2-1)(1) - x(2x))/(x^2-1)^2 = (x^2 - 1 - 2x^2)/ ( x^4 - 2x^2 + 1) = (- x^2 - 1)/ ( X^4 - 2x^2 + 1) d/dx( x^2 + 2x)/(x^4 - 3x^2 + 1) = ((x^4 - 3x^2 +1)(2x + 2) - (x^2 + 2x)(4x^3 - 6x))/(x^4 - 3x^2 + 1)^2 Graph Note. ​with a function like f(x) = 3/ = 3/x^½ It is easier to rewrite it a 3x^-½ and use the power rule =f’(x) = -(3/2)x^-3/2 Using the quotient rule F’(x) = (x^(½

Step 2 of 3

Chapter 3, Problem 3.2.27 is Solved
Step 3 of 3

Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

Other solutions

Discover and learn what students are asking







Chemistry: The Central Science : Molecular Geometry and Bonding Theories
?In the hydrocarbon (a) What is the hybridization at each carbon atom in the molecule? (b) How many \(






People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Find conditions on a, b, c, and d such that commutes with every 2 2 matrix