Let P3= {polynomials in one variable t of degree at most 3} U {0}. (a) Let...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let P3= {polynomials in one variable t of degree at most 3} U {0}. (a) Let p(t) = a + bt + ct² where a, b, c E R. Compute p'(t) and p'(0). (b) Let H be the set of polynomials p(t) in P3 such that p(0) = 0 and p'(0) = 0. Show that I is a subspace of P3 by verifying the three subspace properties. (c) Let H be the set of polynomials p(t) in P3 such that p(0) = 0 and p'(0) = 0. Show that H is a subspace of P3 by expressing H as a span of finitely many polynomials. (d) Find a basis for H. What is the dimension of H? Let P3= {polynomials in one variable t of degree at most 3} U {0}. (a) Let p(t) = a + bt + ct² where a, b, c E R. Compute p'(t) and p'(0). (b) Let H be the set of polynomials p(t) in P3 such that p(0) = 0 and p'(0) = 0. Show that I is a subspace of P3 by verifying the three subspace properties. (c) Let H be the set of polynomials p(t) in P3 such that p(0) = 0 and p'(0) = 0. Show that H is a subspace of P3 by expressing H as a span of finitely many polynomials. (d) Find a basis for H. What is the dimension of H?
Expert Answer:
Answer rating: 100% (QA)
a We have pt a bt ct so pt b 2ct Thus p0 b b To show that H is a subspace of P3 we need to v... View the full answer
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
Students also viewed these accounting questions
-
Find a basis for M23. What is the dimension of M23? Generalize to Mmn.
-
Let °U = R and let I = Z+. For each n Z+ let An = [-2n, 3n]. Determine each of the following: (a) A3 (b) A4 (c) A3 - A4 (d) A3 A4 (e) (f) (g) (h) y A 1-1 U A
-
Let U = R and let the index set I = Q+. For each q Q+, let Aq = [0, 2q] and Bq = (0, 3q]. Determine a) A7/3 b) A3 B4 c) d) U A
-
If a particular glucose fermentation process is 87.0% efficient, how many grams of glucose would be required for the production of 51.0 g of ethyl alcohol (C 2 H 5 OH)? C 6 H 12 O 6 2C 2 H 5 OH +...
-
Multiple Choice Questions Select the best answer for each of the following. Explain the reasons for your selection. a. Which of the following is not a covered member for an attest engagement under...
-
You are an accountant in the budgetary, projections, and special projects department of American Conductor, Inc., a large manufacturing company. The president, William Brown, asks you on very short...
-
In February 2014, defendant Ibrahim M. Shihadeh, d/b/a Creative Designs Kitchen and Baths, agreed to purchase 25% of his anticipated natural gas needs at a fixed price for the 201415 and 201516...
-
Valdespin Company manufactures three sizes of camping tentssmall (S), medium (M), and large (L). The income statement has consistently indicated a net loss for the M size, and management is...
-
Circle the most appropriate choice for the most optimized MIPS assembly program to implement the following compound expression applying a fall through technique: if (($t1 < 0) || ($t2 < 0)) {$t3++; }...
-
Non-controlling interests of profitable subsidiaries result in a credit item in the income statement and a debit balance in the statement of financial position. True/False
-
You are the manager of an educational facility and have beenasked to predict analyze the electric cost for 2020 based on the following 12 months of Information, You know the electric cost has both...
-
Describe the advantages and disadvantages of the following ways of describing functional requirements. Give examples of when each is used . please use simple words a. brand b. by specification of...
-
analyze the code and give the output of the following code. 3. public class Batman { 4. int squares = 81; 5. public static void main(String[] args) { 6. new Batman().go(); 7. } 8. void go() { 9....
-
what ways do adaptive leadership practices foster a culture of resilience and innovation amidst periods of organizational transition?
-
discuss 2-3 issues, challenges, and/or trends within the transportation and logistics field. You will have to conduct online research to determine the issues, challenges, and trends that have emerged...
-
7. A bond has a face value of $1000, and has 6% annual coupons. It is five years from maturity. If the market is providing a 5% return currently, what is the bond worth? (Before performing the...
-
Sarmiento Inc. (SI) is a new company developed by a group of high school friends to provide social media support and services to organizations wishing to advertise using these tools. Sl is...
-
Give the products of the following reaction, where T is tritium: dioldehydrase Ad- CH CH3C-COH CoIII) coenzyme B12
-
In defining the notion of independence for three events we found (in Definition 3.13) that we had to check four conditions. If there are four events, say E1, E2, E3, E4, then we have to check 11...
-
Related to the merge sort is a somewhat more efficient procedure called the quick sort. Here we start with a list L: a1, a2, . . . , an, and use a1 as a pivot to develop two sublists L1 and L2 as...
-
(a) How many subsets of {1, 2, 3, . . . , 11} contain at least one even integer? (b) How many subsets of {1, 2, 3,. . . . . . . . . , 12} contain at least one even integer? (c) Generalize the results...
-
Draw a cash flow diagram of any investment that exhibits both of the following properties: 1. The investment has a 4-year life. 2. The investment has a 10 percent/year internal rate of return.
-
What is the internal rate of return of the following cash flow diagram? a. 20 percent b. 18.2 percent c. 17.5 percent d. 15 percent $30 $31 0 1 2 3 $30 $15
-
Quilts R Us (QRU) is considering investing in a new patterning attachment with the cash flow profile shown in the table below. QRU's MARR is 13.5 percent/year. a. What is the internal rate of return...
Study smarter with the SolutionInn App