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

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?.

Step by Step Solution

★★★★★

3.36 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

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

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

961-M-L-A-L-S (5587).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

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...

Let m, n be two positive integers. Prove that if m, n are perfect squares, then the product mn is also a perfect square.

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.

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

question is this 5) a) Vi and Vr let there be two 4 subspaces of the finite dimensional V vettor space. Boy V, + Bay V2 = Boy (Kn)+ Boyl Vot(e) show that. b) IR' space's : F-scorbicid) I nem) and F2...

Questions 1 and 2 MTH102A: Mathematics - II X 5 PS3_20.pdf X Course Hero X + 0 X C hello.iitk.ac.in/sites/default/files/mth102a/assignments/problems/PS3_20.pdf ... Apps M Gmail Maps YouTube Translate...

14. Let U1 and U2 subspaces of R U1 = U2 = Let fi be an endomorphism of U and f2 an endomorphism of U2, such that the respective Jordan forms are: U1 = U2 = Determine the Jordan form, the minimum...

Let V be a vector space of dimension n, and let W, W2 be subspaces of V. (a) Assume that W W = {0}. Show that dim(W W) = dim(W) + dim(W). ( where the direct sum W W of two subspaces W and W of a...

Let M and N be subspaces of an inner product space V . We sa~.-r that the space V is the orthogonal direct sum of M and M if M + N = 'U' and M J. N. In this case we writeV= M 63 H. Prove that if an...

Prove the theorem cyclically given Let W,..., W be subspaces of a vector space V. We say that they are independent if, whenever w W,..., WkE Wk with w + +wk = 0, then w = ... = Wk = 0. In this case,...

What happens to reserves at the First National Bank if one person withdraws $1,000 of cash and another person deposits $500 of cash? Use T-accounts to explain your answer.

Explain the following in your own words: Automatic navigation Base relvar Catalog Closure Commit Derived relvar Foreign key Join Optimization Predicate Primary key Projection Proposition...

THE POSTAGE FUNCTION. The graph of the "postage function" for 2 0 1 2 , where x denotes the weight of a package in ounces and f ( x ) the postage in cents, is shown in the accompanying figure....

Brownian Motion Gauss file(s) sim_brownind.g, sim_brownemm.g Matlab file(s) sim_brownind.m, sim_brownemm.m Consider estimating the parameters = {, 2} of the stochastic differential equation dyt = dt...

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

Use properties of determinants (Sec. 3.4) to demonstrate why the diagonal eigenvalue property holds in general for triangular matrices.

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...

Dividends on common stock during Year 2 totaled $4,500. The market price of common stock at the end of Year 2 was $10.88 per share. The company's equity multiplier at the end of Year 2 is closest to:...

Current Attempt in Progress Prepare the following adjusting entries at August 31 for Walgreens. (a) Interest on notes payable of $302 is accrued. (b) Services performed but unbilled total \$1,463....

1)commercial/residential 2)an open-end/a closed end 9. Choosing a real estate investment Comparing Real Estate Investments Suppose Deborah wants to invest in real estate and is considering two...