Consider the subspace W = {u(a) = 0 = u(b)} of the vector space C0[a, b] with
Question:
(a) Show that W has a complementary subspace of dimension 2.
(b) Prove that there does not exist an orthogonal complement to W. Thus, an infinite-dimensional subspace may not admit an orthogonal complement!
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 69% (13 reviews)
a Let V x P 1 be the twodimensional subspace of linear polynomials Every ux C 0 a b can ...View the full answer
Answered By
Muhammad Umair
I have done job as Embedded System Engineer for just four months but after it i have decided to open my own lab and to work on projects that i can launch my own product in market. I work on different softwares like Proteus, Mikroc to program Embedded Systems. My basic work is on Embedded Systems. I have skills in Autocad, Proteus, C++, C programming and i love to share these skills to other to enhance my knowledge too.
3.50+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Consider the subspace W = ({v1, v2, v3, v4}). Find a set S so that (1) S is a subset of W, (2) S is linearly independent, and (3) W = (S). Write each vector not included in S as a linear combination...
-
Consider the subspace W of D, given by W = span (sin x, cos x). (a) Show that the differential operator D maps W into itself. (b) Find the matrix of D with respect to B = {sin x, cos x}. (c) Compute...
-
Consider the subspace W of D, given by W = span (e2x, e-2x). (a) Show that the differential operator D maps W into itself. (b) Find the matrix of D with respect to B = {e2X, e-2x}. (c) Compute the...
-
Several industries located along the Ohio River discharge a toxic substance called carbon tetrachloride into the river. The state Environmental Protection Agency monitors the amount of carbon...
-
In 1978, David Brandt and Dean Somerville incorporated Posilock Puller, Inc. (PPI), to make and market bearing pullers. Each received half of the stock. Initially operating out of McHenry, North...
-
A flywheel is mounted on a vertical shaft, as shown in Fig. 2.76. The shaft has a diameter \(d\) and length \(l\) and is fixed at both ends. The flywheel has a weight of \(W\) and a radius of...
-
Starting from Eqs. (14.60) and (14.61), derive the relations \[\begin{aligned}& R(\tau)=\int_{0}^{\infty} S(f) \cos 2 \pi f \tau \cdot d f \\& S(f)=4 \int_{0}^{\infty} R(\tau) \cos 2 \pi f \tau \cdot...
-
Wanda Lux must select a supplier for a plastic bottle and proprietary dispenser for its new hair shampoo. Three suppliers have placed bids; at Wandas request all bids are for a shipping quantity of...
-
Discuss potential uses for virtualization and cloud computing, and how this might affect an organization's long-term IT strategy. Envision how it will develop over the next 10 years
-
The estimated costs of producing 6,000 units of a component are: Per Unit Total Direct Material $10 $60,000 Direct Labor 8 48,000 Applied Variable Factory Overhead 9 54,000 Applied Fixed Factory...
-
Let W V with dim V = n. Suppose w1........wn, is an orthogonal basis for W and wm+1,... wn is an orthogonal basis for W. (a) Prove that the combination w1,...,wn forms an orthogonal basis of V. (b)...
-
For each of the following matrices A, (i) Find a basis for each of the four fundamental subspaces; (ii) Verify that the range and cokernel are orthogonal complements; (iii) Verify that the corange...
-
There has been a trend for professional sports franchises to build new stadiums and ballparks in urban, downtown venues. An article in Professional Geographer (Feb. 2000) investigated whether there...
-
Enterprise social networking is the application of social network tools to education. True or False
-
List as many brands of cars as you can think of. Group the car brands into target markets. What features of each brand identify its target market?
-
If the newspaper market in Problem 17 were perfectly competitive, what would be the quantity, price, consumer surplus, and producer surplus? Mark each on the graph. The figure illustrates the...
-
Viral marketing can be prevented by using the proper spyware. True or False
-
Business intelligence software supports decision making by presenting visual, interactive views of the state of a business. True or False
-
For the following exercises, use the definition of derivative to calculate the derivative of each function. f(x) = 3x 4 lim h0 f(x+h)-f(x) h
-
Create an appropriate display of the navel data collected in Exercise 25 of Section 3.1. Discuss any special properties of this distribution. Exercise 25 The navel ratio is defined to be a persons...
-
The random variable X has the following probability distribution: X 2 3 5 8 Probability 0.2 0.4 0.3 0.1 Determine the following: (a) P(X < 3) (b) P(X > 2.5) (c) P(2.7 < X < 5.1) (d) E(X) (e) V(X)
-
Determine the probability mass function for the random variable with the following cumulative distribution function
-
Each main bearing cap in an engine contains four bolts. The bolts are selected at random, without replacement, from a parts bin that contains 30 bolts from one supplier and 70 bolts from another. (a)...
-
The blue samurai, a japanese restraurant, has an asset turnover of 3.5 the total assets were 95,000 what are net sales for the blue samurai?
-
Gatekeeper Manufacturing reported 50,000 physical units that were 100% complete for direct materials during the period. In addition, the 50,000 physical units were 100% for conversion costs. In terms...
-
What red flag was overlooked on the Montague Fellowship Expense Report?
Study smarter with the SolutionInn App