9. Let x...,x) be linearly independent solutions of x' = P(t)x, where P is continuous on...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
9. Let x...,x) be linearly independent solutions of x' = P(t)x, where P is continuous on %3D (a) Show that any solution x = z(t) can be written in the form z(1) = cx"(t) +..+ C,x" (1) %3D for suitable constants c1,..., Cy. Hint: Use the result of Problem 12 of Section 7.3, and also Problem 8 above. (b) Show that the expression for the solution z(1) in part (a) is unique; that is, if z(1) = kix"(1) +...+ k,x" (1), then ki Hint: Show that (k - c)x(1) +. the linear independence of x = C1.... Ka = Cn. ...+ (k, - c,)x" (t) = 0 for each i in a <t < B, and use 9. Let x...,x) be linearly independent solutions of x' = P(t)x, where P is continuous on %3D (a) Show that any solution x = z(t) can be written in the form z(1) = cx"(t) +..+ C,x" (1) %3D for suitable constants c1,..., Cy. Hint: Use the result of Problem 12 of Section 7.3, and also Problem 8 above. (b) Show that the expression for the solution z(1) in part (a) is unique; that is, if z(1) = kix"(1) +...+ k,x" (1), then ki Hint: Show that (k - c)x(1) +. the linear independence of x = C1.... Ka = Cn. ...+ (k, - c,)x" (t) = 0 for each i in a <t < B, and use
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Let r = f (θ), where f is continuous on the closed interval [α, β]. Derive the following formula for the length L. of the corresponding polar curve from...
-
In classical mechanics Newton's law can be written in the more familiar form F = ma. The relativistic equation, F = dp/dt, cannot be so simply expressed. Show, rather, that where a ?? du/dt is the...
-
Show that Equation 9.1b can be written in the following form if the pipe fluid is water but the manometry fluid is not (and water from the pipe extends all the way to manometry fluid). Also, sp. gr....
-
Figure 2 shows a 250 kg beam BC at the time instant when a 100 N horizontal force is applied to its end B for 10 s. a. Determine the tension in rods AB and CD at an arbitrary instant during the time...
-
Discuss how the four nontraditional marketing methods would fare in low-context cultures. Explain how the methods match or do not match such a culture. Explain how each would be different in...
-
QUESTION 3: (25 marks) Identify, explain briefly (in 2 sentences maximum for each) and specify the general equation for each of the following multivariate time series and volatility models: a. VAR(p)...
-
Which of the following is designed to identify entry of a nonexistent customer account number? a. sequence check c. completeness check b. field check d. validity check
-
During 2012, Vitos Corporation engaged in two complex transactions to improve the business-selling off a division and retiring bonds. The company has always issued a simple, single-step income...
-
Consider the following spot interest rates for maturities of one, two, three, and four years. r1 = 1-4.7% 2-5.2% r3-5.9% r4 = 6.7% Assuming a constant real interest rate of 2 percent, what are the...
-
Tom Zopf owns and manages a computer repair service, which had the following trial balance on December 31, 2014 (the end of its fiscal year). Summarized transactions for January 2015 were as follows....
-
Penn Corporation produced 5 0 , 0 0 0 units in year 1 and had operating cash flow of $ 2 5 0 , 0 0 0 . In year 2 unit sales are expected to increase to 6 0 , 0 0 0 . The company has a degree of...
-
Currently, ACME Inc. has a capital structure consisting of 35% debt and 65% equity. ACME's debt currently has a 8% yield to maturity. The risk-free rate is 4%, and the market risk premium is 6%....
-
The combining of two different European legal traditions means that, while courts outside Quebec are governed by a common law tradition, in Quebec judges administer: Select one: a.A "mixed system" in...
-
Do you think one memberLLCs offer the same level of protection against claims as a multi-member LLCs? Why or why not? Think as a lawyer, how would you frame your argument to get to the person's...
-
Can I get some help with the following: Social Media Influencers A Social Media Influencer is a user on social media who has established credibility in a specific industry. They have access to a...
-
An abstract is _ _ _ _ _ _ _ _ _ _ _ _ . A long description of the article A short description of the article The citation information for the article A list of contributors to the article
-
You are guaranteed annual payments. The first one is $1,000 at the end of the first year. Afterwards, the payment will grow by 6 percent per year. The opportunity ends after 20 years. Your required...
-
Explain the operation of the dividends received deduction.
-
Find the general real solution to the following homogeneous differential equations: (a) u" + 4u = 0 (b) u" + 6u' + 10u = 0 (c) 2u'" + 3u' - 5u = 0 (d) u"" + u = 0 (e) u"" + 13u" + 36u = 0 (f) x2 u" -...
-
Write down the solution u(t, ) to the initial value problem (a) A non-resonant forcing function at frequency (b) A resonant forcing function at frequency = . (c) Show that, as , the limit of...
-
Find bases for the four fundamental subspaces associated with the complex matrices a. b. c. 2 2 2 1-2i -4 3-i -1 2-i -1+2i -2- 3
-
Under U.S. GAAP, the interest cost associated with borrowings used in the self-construction of a business asset may be capitalized to the balance sheet as part of the self-constructed assets cost...
-
Users of financial statements often describe depreciation expense, depletion expense, and amortization expense as sources of operating cash flows. Discuss the accuracy of this assertion.
-
On December 2, 2006, Pfizer Inc. announced that it was immediately discontinuing clinical trials of its Torcetrapib drug. Subsequent clinical results showed that patients taking the drug suffered a...
Study smarter with the SolutionInn App