A square matrix A of size n is upper triangular if [A]ij = 0 whenever i >

Question:

A square matrix A of size n is upper triangular if [A]ij = 0 whenever i > j. Let UTn be the set of all upper triangular matrices of size n. Prove that UTn is a subspace of the vector space of all square matrices of size n, Mnn.

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 02:37 AM

See More Questions

A square matrix P is called an idempotent if P2 = P. Show that: If P is an idempotent, so is Q = P + AP - PAP for any square matrix A (of the same size as P).
A square matrix A is called idempotent if A2 = A. (The word idempotent comes from the Latin idem, meaning "same;' and potere, meaning "to have power:' thus, something that is idempotent has the "same...
A square matrix is called upper triangular if all of the entries below the main diagonal are zero. Thus, the form of an upper triangular matrix is Where the entries marked * are arbitrary. A more...
Cindy Bagnal, the manager of Cayce Printing Service, has provided you with the following aging schedule for Cayce's accounts receivable: Cindy indicates that the $126,700 of accounts receivable...
In Chapter 4, you learned that when an excise tax is imposed on buyers or sellers in a competitive market, the equilibrium price rises, and the tax payment is shared between buyers and sellers. To...
A company uses 85 circuit boards a day in a manufacturing process. The person who orders the boards follows this rule: Order when the amount on hand drops to 625 boards. Orders are delivered...
An idealized model of the normalized power spectral density of a gas laser oscillating in $N$ equal-intensity axial modes is \[ \widehat{\mathcal{G}}(v)=\frac{1}{N} \sum_{n=-(N-1) / 2}^{(N-1) / 2}...
Missouri Fidelity Union Trust Life Insurance Company stock was trading at $2.63 per share. Eight directors sold their shares for $7.00 per share, conditioned on the resignation of eleven of the...
Matlakala is employed by SnownDeep Inc, as an HR Trainee. She has been medically diagnosed with severe anxiety disorder which sometimes induces temporary paralysis in the event that she suffers a...
On July 1, 2011, Lucinda Fogle created a new self-storage business, KeepSafe Co. The following transactions occurred during the companys first month. July 1 Fogle invested $20,000 cash and buildings...
In C3, the vector space of column vectors of size 3, prove that the set Z is a subspace. T3
Let P be the set of all polynomials, of any degree. The set P is a vector space. Let E be the subset of P consisting of all polynomials with only terms of even degree. Prove or disprove: the set E is...
The classical probability distribution function for a particle in a box of length L is given by P(x) = 1/L. Use this to find (x) and (x2)for a classical particle in such a box.
Builtrite Diving Boards, Inc., is just paid a dividend of $1.50. If the firm's growth in dividends is expected to remain at a flat 4 percent forever, then what is the after-tax cost of common stock...
The total money supply M is the sum of two components: bank deposits D and cash holdings C, which we assume to bear a constant ratio C/D = c, 0 < c < 1. The high-powered money H is defined as the sum...
Imagine that you pay $265 for a 4-year, 4% coupon bond with par value of $265.You intend to hold the bond for 1 year.That is, you are going to buy a 4-year bond and then 1 year later, you'll sell a...
Please provide explanation (a) Suppose you create an equally weighted portfolio (holding weights 1/2) of 2 independent stocks (Cov (i,j)=0). What is the portfolio variance? (b) Suppose you create an...
Please fill out the excel sheet below completely: Cakes Sold per day Average Retail per Cake Cakes Sold per year Gross Sales (year) Rent Utilities Labor COGS (50% of Gross Sales) Total Cost Net...
Emily, who is single, sustains an NOL of $7,800 in 2021. The loss is carried forward to 2022. For 2022, Emilys income tax information before taking into account the 2021 NOL is as follows: *The 2021...
Pearson Education, a publisher of college textbooks, would like to know if students prefer traditional textbooks or digital textbooks. A random sample of students was asked their preference and the...
Let and be distinct eigenvalues of a Hermitian matrix A. (a) Prove that if x is an eigenvector corresponding to and y an eigenvector corresponding to , then x*Ay = x*y and x* Ay = x* y. (b) Prove...
Find a unitary matrix p that diagonalizes A, and determine P-1 AP. 7. 9. 11. 4 1-i 1+i 5 T6 2+i 2-2i 4 3 A-0 11+i 01-i 0
Show that the eigenvalues of a unitary matrix have modulus 1.
(3) Calculate m(R) (volume of R) Given: R is the region of the 3- dim space, defined by: 3 Upper border: Z = 92 (x, y) = 3x+5y3 Lower border: Z = 9, (x,y) = x+y xy projection: D= pr (R) = triangle...
Explain what is Model, Strategy, Algorithm in math teaching? How is it similar/compare to 'algorithm' language of borrow or carry over in subtraction
Directions and Info for Building 1. Use a program where you can draw and type, like pages, or you can draw this out on a piece of paper and take a picture to submit. 2. You will begin with the...

A square matrix A of size n is upper triangular if [A]ij = 0 whenever i >

Question:

Step by Step Answer:

Apply Theorem TSS First the zero vector of M nn is the zero matrix O whos...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions