(a) Show that if L: V V is linear and ker L {0}, then L...

Question:

(a) Show that if L: V → V is linear and ker L ≠ {0}, then L is not invertible.
(b) Show that if rng L ≠ V, then L is not invertible.
(c) Give an example of a linear map with ker L = {0} which is not invertible.

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

If a water wave with length L moves with velocity across a body of water with depth d, as in the figure, then (a) If the water is deep, show that v ≈ √gL / (2π). (b) If the water is...
If a water wave with length L movies with velocity v across a body of water with depth d, as in the figure on page 776. Than (c) Use the Alternating Series Estimation Theorem to show that if L > 10d,...
(a) Show that if a > 0, then the function x xa is strictly increasing on (0, ) to R and that (b) Show that if a lim 0 and limoo lim xoe-00 and limx"_ 0.
Two different compounds have the formulation CoBr(SO4) 5NH3. Compound A is dark violet, and compound B is red-violet. When compound A is treated with AgNO3 (aq), no reaction occurs, whereas compound...
Rosa de la Mar Corporation ships a load of goods via Southeast Delivery Company. The load of goods is lost in a hurricane in Florida. Who suffers the loss? Explain your answer.
Assume a retailing company has two departments—Department A and Department B. The company’s most recent contribution format income statement follows: Total Department A Department B Sales...
If P = 20 kN, determine the average shear stress developed in the pins at A and C. All pins are subjected to double shear as shown, and each has a diameter of 18 mm. A-2 m- m P 30 -2m- B
Classifying variances as favorable or unfavorable Required Indicate whether each of the following variances is favorable or unfavorable. The first one has been done as an example. Item to Classify...
2. Using the definition of the derivative, use an appropriate value of h to approximate the derivative of f'(2) where f(x) = x* 3. Find the derivative for the following functions: (a) f(x) =...
A store maintains data on customers, products and purchase records in three tables: CUSTOMER, PRODUCT, PURCHASE. The store manager wants to know which product is on its maximum discount for each...
Find all its invariant subspaces W R2, as defined in Exercise 7.4.32, of the following linear transformations L: R2 R2: (a) The scaling transformation (2x, 3y)T (b) The shear (x + 3y, y)T (c)...
Use superposition to solve the following inhomogeneous ordinary differential equations: (a) u' + 2u = 1 + cos x (b) u" - 9u = x + sin x (c) 9u" - 18u' + 10u = 1 + ex cos x (d) u" + u' - 2u = sinh x,...
The following table, stored in Smartphone Sales , represents the annual market share of smartphones, by type, for the years 2011, 2012, 2013, 2014, and 2015. a. What conclusions can you reach about...
Fill in the blank field in this text: With the elevation tag selected, you can use the [1]___________________________________ icon to adjust the tag orientation to look at an angled wall.
You cannot adjust the extent of view using the crop region. A) True B) False
You can use any Windows True Type font in Revit. A) True B) False
A user keynote presents an opportunity for user error by selecting the wrong item from a list each time this tool is used. A) True B) False
The Snaps Off option must not be checked in the Snaps dialog box to automatically and accurately select snap points while drawing. A) True B) False
Imagine that you work for a local day-care center. You attend a company meeting to discuss new services that would help the center stand out from its competition. You think you can use the services...
A Alkynes can be made by dehydrohalogenation of vinylic halides in a reaction that is essentially an E2 process. In studying the stereochemistry of this elimination, it was found that...
A drug is assumed to be effective with an unknown probability p. To estimate p the drug is given to n patients. It is found to be effective for m patients. The method of maximum likelihood for...
Prove the following binomial identity Consider an urn with n red balls and n blue balls inside. Show that each side of the equation equals the number of ways to choose n balls from the urn. (:)- . (2...
Lucas27 proved the following general result relating to Exercise 37. If p is any prime number, then (n/j) (mod p) can be found as follows: Expand n and j in base p as n = s0 + s1p + s2p2 + + skpk...
What measures can organizations implement to promote transparency and accountability in the budgeting process, thereby fostering trust and buy-in among stakeholders and facilitating...
Based on the following cost expenditures for the construction of an office / warehouse development ( to include direct and indirect charges ) , calculate the peak financial requirement: Month Monthly...
Carlos has worked very hard through his career as a teacher and is contemplating an early retirement. He already has a pension in place commencing at retirement age but wants to cut back on his...

(a) Show that if L: V V is linear and ker L {0}, then L...

Question:

Step by Step Answer:

a If L were invertible then the solution to Lx b would be unique ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions