Prove that the general solution to a linear system with diagonal coefficient matrix Icirc diag( Icirc raquo 1, Icirc raquo n) is given by u(t) (c1e Icirc raquo 1t, , cne Icirc raquo nt)T Au...

We compute dudt 1 c 1 e 1 t n c ...

Prove that the general solution to a linear system with diagonal coefficient matrix Î = diag(Î»1,... Î»n)

Question:

Prove that the general solution to a linear system with diagonal coefficient matrix Î› = diag(Î»1,... Î»n) is given by u(t) = (c1eÎ»1t,... , cneÎ»nt)T.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 09:15 AM

See More Questions

DE Solution Spaces Recall that the "general solution" of a DE means a family or set of solution functions (y | y satisfies the DE), where each y is a function on the interval determined by the domain...
Write the general solution to the following linear systems in the form (2.26). Clearly identify the particular solution x* and the element z of the kernel. (a) a - y + 3z = 1 (b) (c) (d) (e) (f) (g)...
Show that if u (x) solves xu" + 2u - 4xu = 0, then v(x) = xu(x) solves a linear, constant coefficient equation. Use this to find the general solution to the given differential equation. Which of your...
10 1 Journalize the following transactions for Bigelow Company for the month of October. 31 Oct Stockholders invest cash in the company in exchange for common stock. 5 Oct The company buys a delivery...
What is judicial review? How and when was the power of judicial review established?
Boston Clothing Limited was a private company that experienced cash flow difficulties and hired new management to turn the company around. The company then went public and the shares sold at $15 per...
About 10% of workers (ages 16 years and older) in the United States commute to their jobs by carpooling. You randomly select eight workers. What is the probability that exactly four of them carpool...
In December 2010, Kent Computers management establishes the year 2011 predetermined overhead rate based on direct labor cost. The information used in setting this rate includes estimates that the...
The information for Bland Media Company at the end of the fiscal year, June 30, 20X8 are listed in this spreadsheet . Additional information: Capital were $145000 at May 1, 20X7, additional capital...
What is the output of the following code? public class Main { public static void main(String[] args) { int x = 0; for (x=0;x=5;x++) { System.out.print (x); } } } a. Infinite Loop b. 012345 c. 5 d....
Suppose u(f) and both solve the linear system (a) Suppose they have the same value at any one time t1. Show that they are, in fact, the same solution: for all t. (b) What happens if for some t1 t2....
(ii) Write the general solution to the systems in Exercise 9.1.13 in this form. = Au L1
Show that, when Re p > 1000 and C D is governed by Eq. (3.2-5), the range of feasible velocities for fluidizing spheres of diameter d and density o is Given that f 0.41 under these conditions...
In Problems 25-40, decide on a reasonable means for conducting the survey to obtain the desired information. A supermarket wants to study the buying habits of its customers to find out how often...
What are "baby boomers"? Figure 14.25 The crunch to come... Social Security taxes were raised to build a surplus... Money paid into the system has been greatly exceeding benefits since 1983. Scale in...
Suppose the neck size of men is normally distributed, with a mean of 15.5 inches and a standard deviation of 0.5 inch. A shirt manufacturer is going to introduce a new line of shirts. Assume that if...
Use the formula in Example 1 to determine the sample size in Problems 5-14. The estimated prevalence is $35 \%$, and the desired confidence level is $98 \%$ with a margin of error of $2 \%$.
Identify each distribution in Problems 31-34 as skewed to the right, symmetric, or skewed to the left. If it is also a normal distribution, so state. a. 600 450 300 150 0 Modes 0 1 2 3 4 Median = 4 5...
For the following exercises, find the exact value. cos (/12)
Catherine (aged 42) and Johnson (aged 45) have been married for 12 years. Johnson is a project manager of an event company at a monthly salary of $55,000 with an additional one-month salary of...
We saw in Example 9 that the equation cos x = x has exactly one solution. (a) Use a graph to show that the equation cos x = 0.3x has three solutions and find their values correct to two decimal...
Use graphs to determine which of the functions f(x) = 10x2 and g(x) = x3/10 is eventually larger (that is, larger when is very large).
Use graphs to determine which of the functions f(x) = x4 100 x3 and g (x) = x3 is eventually larger.
Create a segmentation, selection and focus model that allows the PUMA company in Mexico to determine its customer, where to find it and how to generate value given its model. 7) Selection of the most...
Determine if the following values are zeroes polynomial. 4 3 f(x) = x + x-18x - 16x + 32 x+1, +2, +4 -
Cali Windows is a small company that installs windows. Its cost structure is as follows: (Click the icon to view the cost structure.) Calculate (a) the breakeven point in units and revenues and (b)...

Prove that the general solution to a linear system with diagonal coefficient matrix Î = diag(Î»1,... Î»n)

Question:

= Au

Step by Step Answer:

We compute dudt 1 c 1 e 1 t n c ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions