Graphs of linear systems, Consider the linear system x' =

Graphs of linear systems

Reference no: EM13122261

Consider the linear system x' = Ax, where A is a n x n real matrix. If x = x(t) is a solution of the linear system, we define:

G(x) = {x(t) : t E R),

which is the set of points on the solution curves x=x(t) in R^n. The set G(t) is called the graph of x = x(t) .

Show that if x(1) = x(1)(t) and x(2) = x(2)(t) are any two solutions of the linear system, then either the intersection of G(x1) and G(x2) is empty, or G(x1) = G(x2), that is their graphs are either disjointed or the same.

Reference no: EM13122261

Questions Cloud

Income distribution diagrams : A study of family income is studied through a sample of 500 randomly selected families. The results can be summarized as the mean family income was 41,000 the median income was 29,000.

Return on stockholders equity : Network Communications has total assets of $1,400,000 and current assets of $600,000. It turns over its fixed assets 4 times a year. It has $300,000 of debt. Its return on sales is 5 percent. What is its return on stockholders' equity?

Important information about probability -random selection : Important information about Probability : Random Selection, A man has been guessing colors of cards drawn from a standard deck of cards. During the first 50 draws he kept track of the number of cards of each color

Explain study to reduce maximum error of estimate : If he were to conduct a second study to reduce the maximum error of estimate to 6, about how many hard drives should he include in his new sample?

Graphs of linear systems : Consider the linear system x' = Ax, where A is a n x n real matrix. If x = x(t) is a solution of the linear system, we define:

Determining the nearest integer : Use the following graph of a function f to determine x or y to the nearest integer as indicated. Some problems may have more than one answer.

Illustrate what is the production for each : Illustrate what is the production (output per hour) for each alternative? Illustrate what is the productivity (output per labour hour)?

Calculate the final temperature of the mixture : A 14.0-g sample of ice at -18.0°C is mixed with 122.0 g of water at 87.0°C. Calculate the final temperature of the mixture assuming no heat loss to the surroundings.

Stock after the distribution : Dixie Corporation distributes $31,000 to its sole shareholder, Sally. At the time of the distribution, Dixie's E&P is $25,000 and Sally's basis in her Dixie stock is $10,000. Sally's basis in her Dixie stock after the distribution is ??

User Account

All Pages