The trace of a n à n matrix A MnÃn. is defined to be the sum of
Question:
a11 + a22 + + ann.
(a) Compute the trace of
(b) Prove that tr(A + B) = tr A + tr B.
(c) Prove that tr(A B) = tr(BA).
(d) Prove that the commutator matrix C = A B - B A has zero trace: tr C = 0.
(e) Is pan (c) valid if A has size m à n and B has size n à m?
Transcribed Image Text:
211 303 114 3 2
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (12 reviews)
a i 4 ii 0 b c The diagonal entries of AB are t...View the full answer
Answered By
Bhartendu Goyal
Professional, Experienced, and Expert tutor who will provide speedy and to-the-point solutions. I have been teaching students for 5 years now in different subjects and it's truly been one of the most rewarding experiences of my life. I have also done one-to-one tutoring with 100+ students and help them achieve great subject knowledge. I have expertise in computer subjects like C++, C, Java, and Python programming and other computer Science related fields. Many of my student's parents message me that your lessons improved their children's grades and this is the best only thing you want as a tea...
3.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
If A = [ajj] is an n à n matrix, then the trace of A, Tr(A), is defined as the sum of all elements on the main diagonal of A, Show each of the following: (a) Tr(cA) = c Tr(A), where c is a...
-
Let U be an m m matrix, V be an n n matrix, and let where 1 is an n n diagonal matrix with diagonal entries 1, 2,..., n and O is the (m - n) n zero matrix. (a) If U = (U1, U2), where U1 has n...
-
The trace of an n n matrix A Mnn is defined to be the sum of its diagonal entries: tr A = a11 +a22 H+. . . + ann. Prove that the set of trace zero matrices, tr A = 0, is a subspace of Mmn?
-
Report Format Market analysis Business - Pizza Vending Machine - Target Place : Universities 1. Target Market University Students in the UK University food 2. Potiential Customers 3. Barrier of entry...
-
1. Describe SEMCOs organizational culture. What artifacts are mentioned in this program that represent and reinforce this culture? What strategies or practices does SEMCO apply to specifically...
-
Explain how an entrepreneur can use staging of investment to both signal the entrepreneurs beliefs and better align the entrepreneurs incentives with the interest of investors.
-
Assuming that one of management's control objectives is to restrict access to securities, which of the following would not be appropriate to satisfy the objective? a. Establish physical barriers over...
-
Spring Waters, Inc., produces bottled drinks. The New York Division acquires the water, adds carbonation, and sells it in bulk quantities to the New Jersey Division of Spring Waters and to outside...
-
a) Take a P.i.B wavefuntion for an electron in an 8 nm long 1D box and consider dividing the entire length of the box in 8 equal segments of 1 nm each. Calculate the ratio of theprobability of...
-
Fifty cities provided information on vacancy rates (in percent) for local apartments in the following frequency distribution. Vacancy Rate (in percent) ......Frequency 0 up to 3 .............. 5 3 up...
-
The commutator of two matrices A, B, is defined to be the matrix C = [A.B] = AB - BA. (1.12) (a) Explain why [A.B] is defined if and only if A and B are square matrices of the same size. (b) Show...
-
Justify the alternative formula for multiplying a matrix A and a column vector x: Ax = x1C1+x2c2 + + xncn. (1.13) where c1,... ,cn are the columns of A and. x1,... ,xn the entries of x.
-
For the following exercises, solve each system by any method. x- 5 121 -6x+ 5 22 || 55 12 55 2
-
Readymade Textiles Ltd. makes and sells baby suits. It has brisk sales in the October-December period as shown by the following sales budget (in units): The firms normal inventory policy has been to...
-
During 2018, Libby Oil and Gas Company completed the last well from its drilling and production platform off the coast of Texas. Unrecovered costs not including decommissioning costs on December 31,...
-
Assume Tony is a 10-year-old fourth grade student with ADHD. The special education evaluation process reveals that Tony has a slightly above average intelligence and ability and a slightly below...
-
On January 1, 2022, John Williams purchased an 8,000-barrel production payment interest from Watershed Oil Company for $800,000. The production payment will be paid out of 1/5 of the working interest...
-
Referring back to question number 5, assume for purposes of discussion that Tony is found not eligible under the IDEA. What would need to be established for him to be eligible under the ADA or...
-
Not a histogram Find a graph other than a histogram that shows the distribution of a quantitative variable in a newspaper, a magazine, or the Internet. 1. Does the article identify the Ws? 2. Discuss...
-
Juanita owns a home in Richardson, TX. She purchases a Homeowners Policy (HO-3) from Farm State Ins. Co. The policy provides $100,000 in liability coverage (coverage E) and $5,000 in Med Pay coverage...
-
Is there a matrix analogue of formula (1.56), namely A T B = B T A? vw = (vw) = wv, W
-
List the diagonal entries of A = 97 2.6 13 37 48 5 9 10 11 14 15 8 12 16,
-
Determine which of the following are bases of R 3 : (a) (b) (c) (d) 1 (-3), ( -2 5
-
Assume that in Bolivia it takes 9 0 hours of labor to produce a ton of salt and 6 0 hours of labor to produce a ton of soybean oil. In addition, assume that in Brazil it takes 8 0 hours of labor to...
-
Should governors have centralized power, particularly when dealing with crisis situations? Or should the formal power of the governor remain relatively weak? (You are required to write 100-150 words)
-
Each scoop of ice cream costs $ 6 . Your benefit associated with each scoop decreases with each additional scoop because you start to get a stomach ache. How many scoops of ice cream should you eat...
Study smarter with the SolutionInn App