Let V and W be vector spaces of dimensions n and m. Show that the space L(V,W)

Question:

Let V and W be vector spaces of dimensions n and m. Show that the space L(V,W) of linear maps from V to W is isomorphic to Mm×n.

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 02:03 AM

See More Questions

Let V and W be vector spaces. If X is a , subset of V, define X = [T in L(V, W) | T(v) = 0 for all v in X) (a) Show that X is a subspace of L(F, IV). (b) If Xcxu show diat X. (c) If U and U\ are...
Let V1, V2, and V3 be vector spaces of dimensions n, m, and p, respectively. Also let L1: V1 V2 and L2: V2 V3 be linear transformations. Prove that L2 o L1: V1 V3 is a linear transformation.
1. Let A be an m ( n matrix and let w be a vector in that satisfies the equation Ax = 0. Show that for any scalar c, the vector cw also satisfies Ax = 0. [That is, show that A(cw) = 0.] 2. Let A be...
You name the catastrophe, and JIT has been through it and survived. Toyota Motor Corporation has had its world-renowned JIT system tested by fire. The massive fire incinerated the main source of...
Suppose a technological advance reduces the cost of making computers. a. Draw a supply-and-demand diagram to show what happens to price, quantity, consumer surplus, and producer surplus in the market...
How many nations were there in 2005? a. 293 b. 193 c. 93 LO.1
Trendstop has been operating for over fifteen years. What inspired you to set up the company? LO.1
On March 1, Jordan Company borrows $90,000 from Ottawa State Bank by signing a 6-month, 8%, interest-bearing note. Instructions Prepare the necessary entries below associated with the note payable on...
The following data was prepared by the Sunland Company Total Variable Fixed Sales price $24/unit Direct materials used $ 94,050 $ 96,000 $ 108,640 $ 13,260 $ 95,380 $ 23,500 $ 13,900 59,600 Direct...
2 nd note: Since tax planning requires a wide range of knowledge in tax, you would need to review material from multiple prior lectures in this course to complete this homework. Question 1 Addison, a...
Fix domain and codomain spaces. In general, one matrix can represent many different maps with respect to different bases. However, prove that a zero matrix represents only a zero map. Are there other...
Show that it follows from the prior questions that for any six transformations t1, . . . , t6 R2 R2 there are scalars c1, . . . , c6 R such that c1t1 + . . . + c6t6 is the zero map.
What method can an IT project manager invoke to ensure that third parties will reach 100 percent completion on a project? A. Retain payment until the integrator reports the project is finished. B....
Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per...
Danny Imasuen is a 37-year-old student working in Quebec. His wages for the current weekly pay period are $580.00. The employer pays $22.00 for life insurance premiums and $190.00 for group medical...
ty: Calculating the WACC Excel Activity: Calculating the WACC Here is the condensed 2021 balance sheet for Skye Computer Company (in thousands of dollars) Current assets 2021 $2.000 Net fixed assets...
need help completing my one-month project. anyone willing help me. Ellipses Corp One Month Project Ellipses Corp is a small business that operates in Herndon, VA. The company is located at10 Period...
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include...
Compute logb 2 (b 4 ).
(a) Water flows through the nozzle of a garden hose. Find an expression for m in terms of line pressure P 1 , ambient pressure P 2 , inside hose diameter D 1 , and nozzle outlet diameter D 2 . Assume...
The sine function sin x has the property that the square of itself plus the square of its derivative is identically equal to one. Find the most general function that has this property.
The rate at which the volume of a mothball evaporates from solid to gas is proportional to the surface area of the ball. Suppose a mothball has been observed at one time to have a radius of 0.5 in....
Four bugs sit at the comers of a square carpet L in. on a side. Simultaneously, each starts walking at the same rate of I in/sec toward the bug on its right See Fig. 1.3.9(a). (a) Show that the bugs...
why would an auditor want to complete dual-purpose tests? what procedure can be put into place to help prevent fraud? List 4 procedures.
Based on the following information, calculate sustainable growth rate for Groot, Inc.: Profit margin= 7.1% Total asset turnover = 1.90 Total debt ratio = .45 Payout ratio = 20% What is the ROA here?
Consider the following: a call option on a stock has strike price $100, premium of $5 and the current price of the underlying stock is $100. If you buy the call option today, what is your holding...

Let V and W be vector spaces of dimensions n and m. Show that the space L(V,W)

Question:

Step by Step Answer:

Fix bases B and D for V and W and consider Rep BD LV W M mn assoc...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions