Let L, M be linear functions. (a) Prove that rng(L M) rng L. (b) Give

Question:

Let L, M be linear functions.
(a) Prove that rng(L ○ M) ⊆ rng L.
(b) Give an example where rng(L ○ M) ≠ rng L.

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 09:02 AM

See More Questions

Let L, M be linear functions. (a) Prove that ker(L M) ker M. (b) Find an example where ker(L M) ker M.
Prove that the Laplacian operator defines a linear function on the vector space of twice continuously differentiable functions f(x, y). af, lf]%3 af ? 2
Give an example where (f (x) + g(x)) exists but neither f(x) nor g(x) exists. lim
The following information has been extracted from the financial statements of XYZ Ltd for the year ended 31 December 2022: Income Statement Sales revenue: $3,000,000 Cost of goods sold: $1,200,000...
What are the three elements necessary for an effective gift?
For the current year, Parker Games has the following inventory transactions related to its traditional board games. Required: 1. Using FIFO, calculate ending inventory and cost of goods sold. 2....
Consider the signal $f(t)=\sin (7 t)$. Use Matlab to obtain the discrete wavelets transform of this signal.
Shelby Corporation purchases 90% of the outstanding stock of Borner Company on January 1, 2011, for $603,000 cash. At that time, Borner Company has the following stockholders equity balances: common...
How could EMS services play a role in advancing the CCMC (Committee on the cost of medical care) guideline advocating for the extension of all basic public health services to the entire population?
Use the web to find out more about the Agile Methodologies. Write a report on what the movement toward agility means for the future of systems analysis and design.
Answer Exercise 7.4.2 for the Volterra integral equation where a ¤ t ¤ b. Exercise 7.4.2 The Fredholm Alternative of Theorem 5.55 first appeared in the study of what are now known as...
Let L: U V be a linear function, and let W U be a subspace of the domain space. (a) Prove that Y = {L[w] | w W} rng L V is a subspace of the range. (b) Prove that dim Y dim W. Conclude that a...
For 1979 through 1998, the net rate of investment income for U.S. life insurance companies was as follows. What was the mean net rate of investment income for this period? The median? Year Percentage...
You have been asked to prepare a schedule of accounts payable. The accounts payable ledger shows the following account balances: Applebaum Associates $ 0 Carlson Company (490) Berkins Inc. 975 Donald...
What is an example of a cost that is relevant in a long term decision, but not a short term decision?
What dollar amount will Gottsbucks show as an asset on its December 31, 2018 Balance Sheet for the Selfie Stick stock, if it owns 10% of the stock of Selfie Stick, and the shares are treated as a...
An investigator has received an NIH grant to work on a study involving an FDA-regulated drug. What financial information must the investigator disclose, and to whom, in order to satisfy the NIH...
Critically discuss that why Pakistan's economic growth continues to be "Balance- of - Payments" constraint which is one you of think that the cose causes to keep the foreign exchange reserves under...
What are the seven factors that should be considered in selecting a file organization?
The outer loop controls the number of students. Note that the inner loop of this program is always executed exactly three times, once for each day of the long weekend. Modify the code so that the...
(From vos Savant26) A reader of Marilyn vos Savants column wrote in with the following question: My dad heard this story on the radio. At Duke University, two students had received As in chemistry...
Barbara Smith is interviewing candidates to be her secretary. As she interviews the candidates, she can determine the relative rank of the candidates but not the true rank. Thus, if there are six...
Show that
1. How many meters are there in 110 yards? 2. What is the equivalent length in inches of 2.5 m? 3. The weight of an object is 2.5 lb. What is the equivalent force and mass in the SI system of units?
An object is moving on a circular path of radius 3 . 0 meters at a constant speed. The time re revolution is 4 . 7 s. What is the acceleration of the object?
If the emitted infrared radiation from the asteroid Ceres, have a wavelength of maximum intensity at 20,000 nm, what is the temperature of Ceres assuming Wien's Law?

Let L, M be linear functions. (a) Prove that rng(L M) rng L. (b) Give

Question:

Step by Step Answer:

a If b rng L o M then b L o ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions