FREE Trial

Let M,N be subspaces of Rn. The perp operator acts on subspaces, we can ask how it interacts with other

Question:

Let M,N be subspaces of Rn. The perp operator acts on subspaces, we can ask how it interacts with other such operations.
(a) Show that two perps cancel: (M┴)┴ = M.
(b) Prove that M  N implies that N┴ ⊂ M┴.
(c) Show that (M+ N)┴ = M┴ ∩ N?.

This problem has been solved!


Do you need an answer to a question different from the above? Ask your question!

Step by Step Answer:

Answer rating: 75% (8 reviews)

a We will show that the sets are mutually inclusive M M and M M For the first if then by the definit…View the full answer


answer-question
Answered By
tutor-profile-image
Dinesh F
I have over 3 years of professional experience as an assignment tutor, and 1 year as a tutor trainee.
5.00+ 1+ Reviews 10+ Question Solved
Related Book For  answer-question
Linear Algebra

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books
View Solution
Create a free account to access the answer
Cannot find your solution?
Post a FREE question now and get an answer within minutes. * Average response time.
Question Posted: June 01, 2016 02:10:05
See More Questions

Students also viewed these Linear Algebra questions

Q:
Let U and W be subspaces of Rn. Define their intersection U W and their sum U + W as follows: U W={X in Rn | X belongs to both U and W}. U+ W= {X in Rn | X is a sum of a vector in U and a vector in...
A:
b First 0 is in U W because 0 0 0 and 0 is in both U and W Now suppose that P and......
Q:
Let m, n be two positive integers. Prove that if m, n are perfect squares, then the product mn is also a perfect square.
A:
Proof Here we provide a direct proof Since m n are perfect......
Q:
Let U and W denote subspaces of Rn, and assume that U W. If dim W = 1, show that either U = {0} or U = W.
A:
We have 0 U W where dim 0 0 and dimW 1 Hence dimU is a......
Q:
Certain merchandising transactions for Yule Park Gifts are listed below. November 2: Purchased 110 souvenir calendars at $9 each from Aloha Co. for cash Nov 4: Paid shipping costs $38 for the...
A:
Journal Entries on Perpetual Inventory Basis Journal Entries on Periodic Inventory Basis Date Partic......
Q:
You were planning to spend Saturday working at your part-time job, but a friend asks you to go skiing. What is the true cost of going skiing? Now suppose you had been planning to spend the day...
A:
If you are thinking of going skiing instead of working at your part time job the......
Q:
Consider an air solar collector that is 1 m wide and 5 m long and has a constant spacing of 3 cm between the glass cover and the collector plate. Air flows at an average temperature of 45?C at a rate...
A:
Air enters the constant spacing between the glass cover and the plate of a solar collector The press......
Q:
For each of the following lists of premises, derive the indicated conclusion and complete the justification. In problems 4 and 8 you can add any statement you choose.
A:
To derive the indicated conclusion using the given premises and the conjunction Conj rule you......
Q:
Determining materials price and usage variances Gwen's Florals produced a special Mother's Day arrangement that included six roses. The standard and actual costs of the roses used in each arrangement...
A:
a Actual cost per unit Standard cost per unit x Actual units 2 24 2 34 x 7......
Q:
Margie Frump is employed as a teacher. She occasionally purchases items that she uses in the course of her employment that are subject to depreciation. Assets held by Margie at 30 June 2021: Margie...
A:
1 Computer Cost 3 600 Adjustable value at 30 6 21 1 200 Effective life 5 years Depreciation method p......
Q:
Using the information from P6-6A and P6-7A for Veryclear Glassware (California Employer Account Number 999-9999-9), complete the following State of California Form DE-9, Quarterly Contribution and...
A:
QUARTERLY CONTRIBUTION EDD Development Department RETURN AND REPORT OF WAGES State of California REMINDER File your DE 9 and DE 9C together PLEASE TYP......
Q:
Suppose that are such that for all complements the projections of into M along N are equal. Must (If so, what if we relax the condition to: all orthogonal projections of the two are equal?) V1, V2 R"
A:
The two must be equal even only under the seemingly weaker conditio......
Q:
The material in this subsection allows us to express a geometric relationship that we have not yet seen between the range space and the null space of a linear map. (a) Represent f : R3 R given by...
A:
a The representation of is this By the definition of f and this second description exactly says thi......
Q:
In Exercises 2738, evaluate each function at the given values of the independent variable and simplify. a. b. c. f(x) |x + 31 x + 3
A:
a b......
Q:
Assume a stock is currently selling for Rs 44.62 per share at the start of 2022. For this company, the analysts' consensus regarding annual growth rate of dividend is 4.6%, and it is likely to remain...
A:
To calculate the company s current net profit margin you ll need to find the net profit and then divide it by the revenue In this case you don t have......
Q:
A 10-year, $1,000 par value bond makes three types of payments over a 10-year period.In all years the bond's YTM (r) has an annual 7.5%.Compounding for the 10 years is semi-annual. Years 1 - 5:Bond...
A:
SOLUTION To calculate the price of the bond today we need to discount the future cash flows generate......
Q:
a. Explain the difference between Clustered Index and Non-Clustered Index. b. Explain what are the advantages and disadvantages with the Index
A:
Clustered Index A clustered index determines the physical order of data rows in a table There can only be one clustered index per table It organizes t......
Q:
The section of a beam with hollow circle at its center for 6 m. Unit weight of concrete is 24 kN/m3 . Concrete compressive strength, fc = 28 MPa and fct = 2.8 MPa. In this problem, b1 = 250 mm, b2 =...
A:
Click to View...
Q:
Nippon Airlines needs to borrow 220m USD. It can borrow USD and JPY at 8% and 7% respectively. Boeing needs to 24.2b JPY. It can borrow USD and JPY at 6% and 7% respectively. Current exchange rate is...
A:
SOLUTION To calculate the cost......
Q:
A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 150 m/s. How far short of the target should it...
A:
Model We will use the particle model for the food pac......
Q:
Given find the value of k. es 1 e kx dx = 1 4'
A:
The integral you ve provided is e 2 to e 8 1 kx dx 1 4 To find the value of k we ne......
Q:
The eigenvalues of an upper triangular matrix and those of a lower triangular matrix appear on the main diagonal. Verify this fact for the matrices in Problems a to c. a. b. c. 0 3 040 100
A:
a The characteristic polynomial is Hence the eigenvalues are 1 1 which......
Q:
Use properties of determinants (Sec. 3.4) to demonstrate why the diagonal eigenvalue property holds in general for triangular matrices.
A:
As we proved in Section 3 4 Problem 15 the determinant of an n n tri......
Q:
For Problems a to b, let A be a square matrix and determine the following facts about its transpose. a. Show that A is invertible if and only if AT is invertible. b. Show that A and AT have the same...
A:
a A matrix A is invertible if and only if det A 0 We shall show that A A T suffices to prove that A......
Privacy Vulnerabilities And Data Security Challenges In The IoT 1st Edition - ISBN: 0367334399 - Free Book