Question: Prove that if A and B are n n matrices, then (a) tr(KA) = k tr(A) + tr(B) (b) tr(AB) = tr(BA)

Prove that if A and B are n × n matrices, then
(a) tr(KA) = k tr(A) + tr(B)
(b) tr(AB) = tr(BA)

Step by Step Solution

★★★★★

3.34 Rating (184 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a Let the ij th entry of A be a ij Then tr A a 11 a 22 a nn so that t... View full answer

blur-text-image
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)

Word file Icon

938-M-L-A-E (1098).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(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 =...

Q:

Prove that if A and B are skew-symmetric n n matrices, then so is A + B.

Q:

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...

Q:

Prove that if A and B are n n matrices, then tr (AB) = tr (BA).

Q:

I need to see how 28 36 and 47 are done please. 35. (a) then so is A + B. 17. Prove Theorem 3.2(a)-(d). 18. Prove Theorem 3.2(e)-(h). (b) Prove that if A is a symmetric non matrix, the is KA for any...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

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...

Q:

Solve in a clear page with details : 2. a) True or False: A, B are n by n matrices, k non zero scalar and kA invertible: (2 points) i) AB = BA, ii) ( KA) -1 = KA-1, iii) (AB) T = ATBT, iv) det(kA) =...

Q:

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Q:

For each of the following situations, calculate the amount of bond discount or premium, if any. a. Holt Co. issued $70,000 of 6 percent bonds at 101 . b. Janus, Inc., issued $100,000 of 10-year, 6...

Q:

Choose a topic that can be applied to one of the following economic concepts. (Possible curves: Lorenz curve, marginal product of labor curve, labor demand and supply curves, utility function and...

Q:

% Par metros del algoritmo NP = 1 0 ; % Tama o de la poblaci n ( soluciones candidatas ) D = 1 0 ; % N mero de variables ( cada soluci n candidata es un vector de D dimensiones ) MAX _ GEN = 3 0 0 ;...

Q:

This baseline project schedule visibility to the project team defines satisfactory performance for the project. True or false?

Q:

Let V be an inner product space. If u and v are vectors in V, Show that (u, v) = ||u + v||2 -1/4 ||u-v||2

Q:

Let V be an inner product space and u a fixed vector in V. Prove that the set of all vectors in V that are orthogonal to u is a subspace of V.

Q:

If V is an inner product space, prove that the distance function of Definition 5, 3 satisfies the following properties for all vectors u, v, and w in V: (a) d(u. v) 0 (b) d(u, v) = 0 if and only if...

Q:

i need help solving this problem personal scanner to create the PDF. In a random sample of 50 cross-country runners, the mean body mass index (BMI) was 27.7 and the standard deviation was 6.12....

Q:

Required information [The following information applies to the questions displayed below.) Brodrick Company expects to produce 20,400 units for the year ending December 31. A flexible budget for...

Q:

1.The average weight for an adult female Beagle is 26 pounds 8 ounces with a standard deviation of 3 pounds 4 ounces. If the weights of Beagles are approximately normally distributed: A.What is the...