Let L1 : U V and L2 : V W be linear transformations, and let

Question:

Let L1 : U → V and L2 : V → W be linear transformations, and let L = L2 ° L1 be the mapping defined by
L(u) = L2(L,(u))
for each u ∈ U. Show that L is a linear transformation mapping U into W

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:53 AM

See More Questions

Let L1: U v1 and L2: U V2 be linear maps between inner product spaces, with V1, V2 not necessarily the same. Let K1 = L1* L1, K2 = L2* L2. Show that the sum K = K1 + K2 can be written as a...
Let L1, L2, and S be as in Exercise 3. Find the following: (a) (L1 o L2) ([u1 u2 u3]) (b) (L2 o L1) ([u1 u2 u3]) (c) The representation of L1 o L2 with respect to S (d) The representation of L2 o L1...
Let V -T U -s W be linear transformations. If ST is onto, show that S is onto and that dim W < dim U
Sodium nitrite (NaNO2) reacted with 2-iodooctane to give a mixture of two constitutionally isomeric compounds of molecular formula C8H17NO2 in a combined yield of 88%. Suggest reasonable structures...
What are the benefits of using a nominal anchor for the conduct of monetary policy?
John installed a new roof on his friends house in return for a used truck worth $8,000. How much income must John report on his tax return for his services?...
Carburettor is used for (a) S.I. engine (b) C.I. engine (c) Gas engine (d) none of the above
The following information pertains to Leslies Floor Store sales on account and accounts receivable. Accounts receivable balance, January 1, 2012 ....... $ 52,500 Allowance for doubtful accounts,...
An investment of $21700 is accumulated at 5.24% compounded quarterly for three and one-half years. At that time the interest rate is changed to 6.12% compounded monthly. How much is the investment...
PART B Betsy has come back to you with some changes to be made to the draft budget. These changes will have come via email or feedback on your hard copy draft. Betsy also thinks that you have over...
Let L be a linear operator on a vector space V. Define Ln, n 1, recursively by L1 = L Lk+ l(v) = L(Lk(V)) for all v V Show that L" is a linear operator on V for each n > 1.
Determine the kernel and range of each of the following linear operators on P3. (a) L(p(x)) = xp'(x) (b) L(p(x)) = p(x) - p'(x) (c) L(p(x)) = p(0)x + p(1)
If an audit client does not have prenumbered checks, what type of misstatement has a greater chance of occurring? Under the circumstances, what audit procedure can the auditor use to compensate for...
A chip manufacturer makes video gaming chip that can be sold for $50. The chip material cost is $15 for each chip. The operations costs of the chip manufacturer (administration etc.) is $100000. The...
Please describe what a Galera cluster is and how it works. In your description, compare a Galera cluster to a Windows server cluster and the strengths and weaknesses of each synchronous and...
Ivanhoe Inc. made a $23000 sale on account with the following terms: 1/15, n/30. If the company uses the net method to record sales made on credit, how much should be recorded as revenue?
What is a product that is characterize as being 'out of control' from a statistical process control perspective. How could statistical process control be used to assign the cause of this quality...
Three capacitors are connected in parallel. Each has plate area A = 6.0010 -2 m 2 and plate spacing d = 2.6010 -3 m . What must be the spacing of a single capacitor of plate area A if its capacitance...
For the following exercises, graph each side of the equation to find the zeroes on the interval [0,2). 20cos 2 x + 21cos x + 1 = 0
You are standing at x = 9.0 km and your assistant is standing at x = 3.0 km. Lightning bolt 1 strikes at x = 0 km and lightning bolt 2 strikes at x = 12.0 km. You see the flash from bolt 2 at t = 10...
In each case either prove the assertion or give an example showing that it is false. (a) If A and B are both invertible, then A + B is invertible. (b) If A4 = 3I, then A is invertible. (c) If AB = B...
For each of the following elementary matrices, describe the corresponding elementary row operation and write the inverse. a. b. c. d. e. f. 103 E=1010 00 1 00 1 E=1010 1 00 0 12 0 100 100 E-1-210 001...
In each case find invertible U and V such that where r = rank A (a) (b) (c) (d) UAV=1 0 0 0 1-1 2-2 4 21 2 1-1 21 A=12-I 03 0 1-41 110- A=1 3 2 1 1 1013
If the nominal interest rate is 14%, and inflation is 4%, what is the real interest rate? 22.A bond investment yielded 8%. If inflation was 3%, what real return did the bond offer? 23.The following...
Bierce Corporation has two manufacturing departments--Machining and Finishing. The company used the following data at the beginning of the year to calculate predetermined overhead rates: Estimated...
Discuss how communication channels have changed over the years due to technology.

Let L1 : U V and L2 : V W be linear transformations, and let

Question:

Step by Step Answer:

If v 1 v 2 V then L v 1 v 2 L 2 L 1 ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions