missy9225
23.08.2019 •
Mathematics
linear algebra section 4.2 subspaces
1. let w1 and w2 be subspaces of a vector space v . define w to be the set of vectors in v oftheformw1+w2 wherew1 ? w1 andw2 ? w2.
(a) show that w is a subspace of v .
(b) show that w1 and w2 are subspaces of w
Solved
Show answers
More tips
- L Leisure and Entertainment How to Land on the Moon: Your Comprehensive Guide...
- T Travel and tourism How to Use a Compass: A Beginner s Guide...
- C Computers and Internet Porn Banner: What It Is and How to Get Rid Of It?...
- F Food and Cooking How many stages of coffee roasting are there?...
- F Food and Cooking From Latte to Espresso: Which Coffee Drink is the Most Popular on Earth?...
- F Food and Cooking Experts Name Top 5 Healthiest Teas...
- C Computers and Internet Google Search Tips and Tricks: Everything You Need to Know...
- H Health and Medicine Discover the Hidden Principles and Real Results of the Japanese Diet...
- H Health and Medicine Liver Cleansing - Rejuvenation for the Body?...
- S Style and Beauty Is Photoepilation the Solution to Unwanted Hair Forever?...
Answers on questions: Mathematics
- M Mathematics 5c+1/2(3/4-2/3c) SIMPLIFY PLEASE...
- M Mathematics Mike by £6 of melon janet by his 5 pounds of pineapple which never sends compares amount that my and janet spend...
- M Mathematics What is the solution to the system of equations? 2x – y = 7y = 2x + 3...
- M Mathematics Identify the percent of change as an increase or a decrease. 120 meals to 52 meals...
- M Mathematics Which of the following is an example of mutualism? a group of piranhas work together to attack a large animal. a mosquito feeds off the blood of another animal and...
- M Mathematics The length of the hypotenuse of a 30-60-90 triangle is 11 2 . how do you find the length of the leg opposite the 30° angle? what is the length of that leg?...
- M Mathematics Circle the equivalent expressions 6x+18-3x-9 6x-3(3x-3) -3(x-3) -6x+3(3+3x)-6x...
- M Mathematics What is the total cost for the carpet install, including the cost of the carpet, the cost of labor, and the additional fee? note: express your answer as a decimal...
- M Mathematics How many hours should it take for the four-person crew to lay the flooring in charlotte s bedroom? note: express your answer as a decimal number and round to the...
- M Mathematics What is -11=7-x in two step equation?...
Ответ:
Proof
Step-by-step explanation:
(a)
- We first have to show that . Since are subspaces, it holds that , hence .
- Second, we have to show that is closed under sum and scalar multiplcation. First, let us take .
Since a, b belong to , we can find and such that
Therefore,
since are vector subspaces of , it holds that
, which shows us that W is closed under sum.
On the other hand, let us take and . We already know that
where and . Moreover,
,
hence
belongs to , which shows that is closed under scalar multiplication.
(b) It is clear that . Moreover, since are subespaces of , they are closed under sum and scalar multplication, this propertie is remains true for as subsets of , which tells us that are subspaces of .
Ответ: