Let A be an n n matrix of numbers, and let P be an n n nonsingular matrix of numbers. Let B=P1 AP. Show that eBt = P1 eAt P. From this, conclude that eAt = PeBt P1 .
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Calculus notes of 9/26/16 3.11 Related Rates Suppose a spherical weather balloon is filled with gas at a rate of 150 ft /min. What is the rate of change of its radius when the radius is 20 ft We are given / = 150: Volume increases by 150 ft /min. 3 dt dr We want / whedtr = 20 We need an equation relating V to r. 3 For a sphere, V = 4/3ᴨr dv 2 dr Different Rating time / = 4/3dt* 3r / (implicitdtifferentiation) 2 Or V’ = 4/3ᴨ * 3r r’ Solving for / , dt = dt(4ᴨr ) * /2 dvdt = 1/(4ᴨ * 20 ) * 150 = (3/32ᴨ) ft/min = 0.02984 ft/min Procedure: 1. Identify known rates and desired rates. Label what you alread
Textbook: Advanced Engineering Mathematics
Author: Peter V. O'Neill
The full step-by-step solution to problem: 10.52 from chapter: 10 was answered by , our top Math solution expert on 12/23/17, 04:48PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 23 chapters, and 1643 solutions. Since the solution to 10.52 from 10 chapter was answered, more than 238 students have viewed the full step-by-step answer. The answer to “Let A be an n n matrix of numbers, and let P be an n n nonsingular matrix of numbers. Let B=P1 AP. Show that eBt = P1 eAt P. From this, conclude that eAt = PeBt P1 .” is broken down into a number of easy to follow steps, and 39 words. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 7. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781111427412.