Define T: Pn Pn by T(p) = p(x) + xp'(x) for all p in Pn. Show
Question:
Show that ker T = {0} and conclude that T is an isomorphism. [Write p(x) = a0 + a1x + ∙ ∙ ∙ ∙ + anxn and compare coefficients if p(x) = - xp'(x).]
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 61% (13 reviews)
If px is in ker T then px xp x If we write px a 0 a 1 x a n x n this becomes a 0 ...View the full answer
Answered By
Allan Simiyu
I am an adroit Writer. I am a dedicated writer having worked as a writer for 3 years now. With this, I am sure to ace in the field by helping students break down abstract concepts into simpler ideas.
5.00+
8+ Reviews
54+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Define T: Pn R by T[p(x)] = the sum of all the coefficients of p(x). (a) Use the dimension theorem to show that dim(ker T) = n. (b) Conclude that (x - 1, x2 - 1,..., xn - 1} is a basis of ker T.
-
Let T: P2 R3 be defined by T(p) = (p(0)), p(1),(p(2)) for all p in P2. Let B = {1,x, x2}and D = [(1,0,0),(0,1,0),(0,0,1)] (a) show that MDB (T) = And conclude that T is an isomorphism. (b) Generalize...
-
Let P, Q and f, g be as in Exercise 3 and, without loss of generality, we suppose that the dominating measure is a probability measure (e.g,. = (P + Q)/2). Define ( by ( = ( ( (fg)1/2 d , and show...
-
Given this expression, what can we say about the problem domain? tBoat (BoatSerialNo, BoatType, Manufacturer, Price, Customer, Date Of Sales Rep) SalesRep should not be in the expression at all...
-
List five examples of specific operational audits that can be conducted by an internal auditor in a manufacturing company.
-
Air enters an adiabatic compressor at \(150 \mathrm{kPa}\) and \(350 \mathrm{~K}\) at a rate of \(0.8 \mathrm{~m}^{3} / \mathrm{s}\) and leaves at \(700 \mathrm{kPa}\) and \(500 \mathrm{~K}\)....
-
Indicate the purposes served by production orders in the production cycle.
-
Portman Corporation has retained earnings of $675,000 at January 1, 2012. Net income during 2012 was $1,400,000, and cash dividends declared and paid during
-
2. Yorkton Supply Company sells bicycle accessories. For one of the products, safety reflectors, they have the following inventory transactions. For the month of June, what would be the Cost of Goods...
-
In a circuit with impressed voltage E(t) and inductance L, Kirchhoff's first law gives the relationship E(t) = L di/dt + Ri, Where R is the resistance in the circuit and i is the current. Suppose we...
-
Let V consist of all sequences [x0, x1, x2,...) of numbers, and define vector operations [x0. x1,.....) + [y0, y1,.....) = [x0 + y0, x1 + y1,.....) r[x0, x1...) = [rx0 > rx1...) Define T: V U and S:...
-
Let T: V W be a linear transformation, where V and W are finite dimehsional. Show that T is onto if and only if there exists a linear transformation S: W V with TS = 1w A [Let {e1,..., er ,..., en}...
-
1. The atomic particle that carries a positive charge is (a) The neutron. (b) The proton. (c) The electron. (d) None of the above. 2. The atomic particle that carries a negative charge is (a) The...
-
A company which makes up its financial statements annually to 31 December, provides for depreciation of its machinery at the rate of 12 per cent per annum using the reducing balance method. On 31...
-
Arthur deals in bicycles. His business position at 1 October was as follows: Capital 3,369 Inventory 306 (3 x Model A bicycles @ 54 and 3 x Model B @ 48) Balance at bank 3,063 Having established good...
-
J. Philip started in business on 1 January 2015 with 60,000 in a bank account. Unfortunately, he did not keep proper books of account. He must submit a calculation of profit for the year ending 31...
-
A vehicle bought on 1 January 2017 cost 36,000. Its useful economic life is estimated at three years and its trade-in value at that point is estimated as being 6,000. During 2019 a review of the...
-
Your bookkeeper extracted a trial balance on 31 December 2016 which failed to agree by 860, a shortage on the credit side of the trial balance. A suspense account was opened for the difference. In...
-
Record journal entries for the following purchase transactions of Flower Company. A. On October 13, Flower Company purchased 85 bushels of flowers with cash for $1,300. B. On October 20, Flower...
-
How do individual companies respond to economic forces throughout the globe? One way to explore this is to see how well rates of return for stock of individual companies can be explained by stock...
-
(a) Show that if A = A-1, then det(A) = 1. (b) If AT = A-1, what is det(A)?
-
Show that if A and B are square matrices, then det = (det A)(det B). 8
-
If A is a nonsingular matrix such that A2 = A, what is det(A)?
-
How does a leader impact an organization's approach to making the more ethical choices? What examples of relativism, the moral philosophy, in action within your organization? Using the Framework for...
-
A battery is used in a physics lab to supply current to a circuit. A voltmeter connected in parallel across the cell reads 5.17 V in an open circuit (figure a) and 4.83 V in a closed circuit (figure...
-
For a non-inverting Op Amp circuits shown below (R1-10K, Rf = 100K2), calculate the expected closed-loop voltage gain and the input impedance. -V2 -15 V V+ + + Vout 741 R1 V1 V3 10k OPAMP 5T VIRTUAL...
Study smarter with the SolutionInn App