Prove that if A and B are n n matrices, then tr (AB) = tr (BA).
Question:
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 78% (14 reviews)
Let A and B be n n matrices Then trAB AB 11 AB 22 AB nn a 11 ...View the full answer
Answered By
SUMAN DINDA
I LIKE TO TEACH STUDENTS. SO, I START MYSELF AS A PRIVATE TUTOR. I TEACH STUDENTS OF DIFFERENT CLASSES. I HAVE ALSO DONE BACHELOR OF EDUCATION DEGREE(B.ED). DURING THIS COURSE I HAD TO TEACH IN A SCHOOL. SO I HAVE A GOOD EXPERIENCE IN TEACHING.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
(a) Give an example to show that if A and B are symmetric n n matrices, then AB need not be symmetric. (b) Prove that if A and B are symmetric n n matrices, then AB is symmetric if and only if AB =...
-
Prove that if A and B are skew-symmetric n n matrices, then so is A + B.
-
Upper Triangular Matrices A square n ( n matrix A = [aij] is called upper triangular if aij = 0 for i > j. (All entries below the main diagonal are zero.) (a) Give three examples of upper triangular...
-
The table lists the actual annual cost y to drive a midsize car 15,000 miles per year for selected years X. (a) Predict whether the correlation coefficient is positive, negative, or zero. (b) Find a...
-
Various financial data for the past two years follow. Calculate the total productivity mea-sure and the partial measures for labor, capital, and raw materials for this company for both years. What do...
-
A room is 6 m by 5 m by 3 m. (a) If the air pressure in the room is 1 atm and the temperature is 300 K, find the number of moles of air in the room. (b) If the temperature rises by 5 K and the...
-
Find the finite difference solution of the problem \[\begin{aligned}& \frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial u}{\partial t} \quad 0 by the explicit method. Plot the solution using...
-
The Gannon Company has budgeted sales revenues as follows: Past experience indicates that 60% of the credit sales will be collected in the month of sale and the remaining 40% will be collected in the...
-
Using the typical floor plan on next page as a base, propose a trunk & branches overhead layout of the ducts serving the typical floor's via mixing mechanical ventilation. 1) Identify different...
-
A news report states that minority children who take advanced mathematics courses in high school have a first-year GPA in college that is equivalent to that of white students. The newspaper columnist...
-
The trace of an n X n matrix A = [aij] is the sum of the entries on its main diagonal and is denoted by tr(A). That is, tr(A) = a11 + a22 + + ann If A and B are n n matrices, prove the following...
-
If A is any matrix, to what is tr (AAT) equal?
-
Determine the functional unit for comparing the life cycle impact of a textbook printed on paper versus one that is delivered electronically. Identify the most important processes in both life...
-
How has mobile grown from a one-way communication between the brand and target to one that is both interactive and engaging?
-
Discuss the pros and cons to a brand of a message going viral.
-
To be a successful member of an IMC campaign, guerrilla marketing must accomplish four specific things. What are they? Define and explain each.
-
Alternative media vehicles have more diverse options than any other advertising and promotional category. What does the advertised message need to relay visually and verbally to strategically express...
-
What is important when writing and designing for mobile?
-
Sam enters a competition run by his local newspaper, the Surrey Times. He wins second prize, an Excel washing machine, which has been manufactured by Excel Appliances Ltd. Sam used the machine for...
-
Explain the buyers position in a typical negotiation for a business. Explain the sellers position. What tips would you offer a buyer about to begin negotiating the purchase of a business?
-
Determine whether A is diagonalizable and, if so, find an invertible matrix P and a diagonal matrix D such that P -1 AP = D. 2 0 0 0 -2 -2
-
Use the method of Example 4.29 to compute the indicated power of the matrix. -5 8 15 -4 7
-
Use the method of Example 4.29 to compute the indicated power of the matrix. -5 -3 -1
-
Can you elucidate the principles underlying genome organization and chromatin structure, including the roles of topologically associating domains (TADs) and chromosomal territories in gene regulation...
-
State three ways of using artificial intelligence and machine learning in marketing and explain each use case with two examples.
-
discuss the principles of population genetics, including allele frequency distributions, Hardy-Weinberg equilibrium, genetic drift, and natural selection, and how these concepts inform our...
Study smarter with the SolutionInn App