Question: 2. Let V be the vector space of all differentiable functions from R to R. Let B={e5t,e5tcost,e5tsint} and consider the subspace W=span(B) of V. (a)

2. Let V be the vector space of all differentiable functions

2. Let V be the vector space of all differentiable functions from R to R. Let B={e5t,e5tcost,e5tsint} and consider the subspace W=span(B) of V. (a) Let D be the differentation operator (i.e., D(f(t))=f(t)) on W. Find the matr representation [D]B,B. (b) Verify Theorem 2.41 (i.e., [Df]B=[D]B,B[f]B ) for the input function f(t)=3e5te5tcost+2e5tsint

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

EnviroWastes year-end is December 31. The information in (a) to (e) is available at year-end for the preparation of adjusting entries: a. Of the $18,500 balance in Unearned Revenue, $3,050 remains...

Hi, I have a linear algebra question. I need your help. Thanks a lot. Let V be the vector space (over (C) of functions f: R + (C, such that the real and imaginary parts of f are innitely...

please prove parts b through f for proof based linear algebra Problem 6. Let V be a vector space. (a) Let (-, -) : V x V -> R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let 2...

Problem 6. Let V be a vector space. (a) Let (-, -) : V x V - R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let 3 = (U1, . .., Un) be a basis of V. Prove that there exists a...

8.1 WRITE on paper for upvote. Section: 25, 32, 33 please 8.1 General Linear Transformations 20. Consider the basis S = {V1, V2} for R', where v, = (-2, 1) and 9. T : Rx - R., where V2 = (1, 3), and...

for part 5 chose one a or b 1. The following matrices are related. A' is row-equivalent to A, and A" is the transpose of A. Use this information to complete the following: N 2 1 -6 00 Co its co 3 A =...

4. Let V be the vector space of all real-valued continuous functions over R. Consider the subspace W = span{1, x, e x }, and let T : W ? W be the linear transformation defined by T(1)=0, T(x)=?x, T(e...

(4) Circle the correct answer or fill in the blanks. (You do not have to give explanations.) (a) Is set of vectors (8,2 sinr, 4 cosx} linearly independent? Circle YES or NO. (b) Is W is a subspace of...

rch Q1 1 Point If A is a singular n X n matrix, then the associated homogeneous system represented by An? = 6 has only the trivial solution. 0 True 0 False Q2 1 Point Let V denote the vector space of...

12:39 1 .0 LTE Done 5 of 5 (3) Let V be the vector space of polynomials of degree at most n. Are the following subspaces? Prove or disprove. (a) All polynomials of the form f(x) = ar", where a is a...

HHelp me to solve the questions as attached below. 3. Consider an economy with A consumers and B rms. Each consumer is endowed with one unit of time and one piece of capital. A representative...

1. An alternating current, i amperes, is given by i = hertz and t the time in seconds. Determine the rate of change of current when t = 30 8 sin(3tft), where f is the frequency in milliseconds, given...

Kramer and Knox began a partnership by investing $60,000 and $80,000, respectively. During its first year, the partnership earned $160,000. Prepare calculations showing how the $160,000 income should...

What is the gross profit margin? Aster Retailers has sales of $520,000 and cost of goods sold of $312,000. What is the gross profit margin? (A) 30% (B) 65% (C) 40% (D) 60% (E)55%

Fiduciary funds are reported A. In both the fund financial statements and the government-wide financial statements. B. As required supplementary information. C. By fund type in the government-wide...