Consider the transformation t : P2 P2 described by x2 x + 1, x

Question:

Consider the transformation t : P2 → P2 described by x2 → x + 1, x → x2 - 1, and 1 → 3.
(a) Find T = RepB,B(t) where B = (x2, x,1).
(b) Find ^T = RepD.D(t) where D = (1,1 + x,1 + x + x2).
(c) Find the matrix P such that ^T = PTP-1.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 02:27 AM

See More Questions

Consider the transformation T: P2 R2 defined by For example, if p(t) = t2 - 6t + 4, then a Prove that T is a linear transformation. b Find a basis for the kernel of T. c Find a basis for the image of...
Consider the transformation T: R2 R4 defined by The RREF of B is Determine dim(Ker(T)) and dim(lm(T)). Is T one-to one? Is it onto R4? T(-) = Bi 0]00 1000
(a) Consider the transformation of ax2 + bx + c in P2 to |a| in P0. Show that it does not correspond to a linear transformation by showing that there is no matrix that maps (a, b, c) in R3 to |a| in...
Marty owns an auto body repair shop. The business has no real value without him and the building is pretty much a mess after being full of paint fumes for all those years but the land is worth...
What are demand deposits and why should they be included in the stock of money?
For each of the following, discuss which data-gathering method(s) are most appropriate and why: a. Examining the adequacy of internal controls in the purchase requisition procedure. b. Identifying...
In a randomly selected sample of women ages 20 34, the mean total cholesterol level is 179 milligrams per deciliter with a standard deviation of 38.9 milligrams per deciliter. Assume the total...
Suppose that AlwaysRain Irrigations marketing department will undertake an intense ad campaign for the bronze sprinklers, which are more expensive but also more durable than the plastic ones....
Your firm has debt worth $250,000, with a cost of debt of 9 percent. It faces a 20 percent tax rate. If an indentical unlevered firm has a total value of 450,000, under Miller and Modigliani model...
Chester has a new design for their product Cone next round that can reduce their material cost of producing units from $8.14 to $7.32. Chester passes on half of all cost savings by cutting the...
Consider this transformation of C3 and these bases. We will compute the parts of the arrow diagram to represent the transformation using two similar matrices. (a) Draw the arrow diagram, specialized...
Let T represent t : C2 C2 with respect to B; B. We will convert to the matrix representing t with respect to D,D. (a) Draw the arrow diagram. (b) Give the matrix that represents the left and right...
Consider a payoff $C$ that will occur in 2 years, taking one of the three possible values $C_{0}, C_{1}, C_{2}$. The short rate lattice for these 2 years is shown in Figure 16.16, with \(d_{i...
Often it is necessary to validate data input by the user and repeat the request for the data in the case where the input of the user is not valid. This can be done by using a do loop, while loop, or...
< Career Preparation Assignment Start Date Jan 15, 2024, 12:00 AM Assessment Traits Requires Lopeswrite Due Date Jan 21, 2024, 11:59 PM Points 25 Assessment Description The purpose of this assignment...
Write the slope-intercept form of the equation of the line described. 4) through: (-5, 0), parallel to y=-- 3 5 5) through: (2,-4), perp. to y=2x-1
4) The mass of the seesaw shown is negligible, and the pivot is frictionless (2 pt) A. Is there a magnitude of force of F2 for which the seesaw will be in equilibrium (yes/no):__ B. If yes, what is...
Music Matters are interested in understanding how their earnings relate to the overall Musical Instrument market. Your manager has asked you to explore the market earnings to support the developments...
Details related to all employees gross earnings, deductions, and net pay for a period are found in the a. Payroll register. b. Individual earnings record. c. General journal. d. Cash payments journal.
On 1 July 2018, Parent Ltd acquired all the shares of Son Ltd, on a cum-div. basis, for $2,057,000. At this date, the equity of Son Ltd consisted of: $ 1,000,000 Share capital 500 000 shares...
Show that if A is a normal matrix then each of the following matrices must also be normal. (a) AH (b) I + A (c) A2
Let (a) Show that {z1, z2} is an orthonormal set in C2. 1 +i and 22
Let A be a real 2 Ã 2 matrix with the property that a21a12 > 0, and let Compute B = SAS-1. What can you conclude about the eigenvalues and eigenvectors of B? What can you conclude about the...
What is the worst case running time of the following sudo codes, in 0- notation? Suppose that all arithmetic operations (including simple multiplication) take a constant amount of time. Justify your...
4. Let G be a pseudorandom generator with expansion factor (n) > 2n. In each of the following cases, say whether G' is necessarily a pseudorandom generator and explain why or why not. Here, "||...
Write the code for the del () method in the following doubly linked list class public class ObjDList { private Obj Node list; private Obj Node tail; public ObjDList() { list = null; tail = null; }...

Consider the transformation t : P2 P2 described by x2 x + 1, x

Question:

Step by Step Answer:

a Because we describe t with the members of B finding the matrix representation is easy gives this ...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions