Question: 2. Let A, B E Mnxn (F). (a) Prove that if A is similar to B, then tr A = tr B. (b) Prove that

2. Let A, B E Mnxn (F). (a) Prove that if A is similar to B, then tr A = tr B. (b) Prove that if A is similar to B, then det A = det B. (c) Prove that if A is diagonalizable over F with eigenvalues A1, . .., An possibly re- peating, then tr(A) = Alt .. . + An and det A = 1 .. . An

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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

Students Have Also Explored These Related Mathematics Questions!

Let A, B E Mnxn (F). (a) Prove that if A is similar to B, then tr A = tr B. (b) Prove that if A is similar to B, then det A = det B. (c) Prove that if A is diagonalizable over F with eigenvalues A1,...

how to solve all parts of question 4 4. Concavity and quasiconcavity a. Let f(x) = x/ for x E R+ +. Notice that x here is a single variable, x E R+ +, not a vector. Using calculus, determine for...

Problem 8 (15 points). Let A, B E Rxxn a. (3 points) Prove that if I - AB is invertible then I - BA is invertible. Note: We do not know anything about invertibility of A and B. b. (3 points) Prove...

how to start and solve each question 1. Let there be two goods with quantities x = (x1.xz) E RE is 3:1 32 0, x2 2 0. Let prices 33 = (ppm) E R$+ i'e p1 > 0.33; > 0. Let the consumer's preferences be...

MAT301 ASSIGNMENT 1 DUE DATE: WEDNESDAY MAY 18, 2016 AT THE BEGINNING OF YOUR TUTORIAL Question 1. Define the following relation on the integers: a b 2|(a b) Prove that this is an equivalence...

Let F be an arbitrary field. The trace of a square matrix M M (F) is tr M := Ei=1 Mii F. (a) Given A Mm (F) and B E Mn (F), verify that tr(AB) tr(A) tr(B). = (b) Prove there are linear operators...

How we proceed f(1). Find a polynomial g(x) in Z[x] such that Ker d = (g(x)). Is there more than one possibility for g(x)? To what familiar ring is Z[x]/Ker o isomorphic? Do this exercise with Z...

Give an example of a function f which satisfies the intermediate-value property on a closed and bounded interval [a, b] but is not continuous on a, 6). () Give an example of a function f which is...

. Answer the following questions. 1. (3 points) In Metropolis only taxicabs and privately owned automobiles are allowed to use the highway betwem the airport and downtown. The market for taxi cab...

Kindly give only correct answers showing your steps 1. (a) Use the Intermediate Value Theorem to show that the equation - sin (x) + sin(x) =-1 has at least two distinct real solutions on (0, ce)....

a) Revenue account for National Life & General Insurance company and determine the closing Life Assurance balance at the end of the year. b) Prepare Balance Sheet as on 31 December 2019 after making...

Two straight lines drewnon the same displacement time graph make angles 30and 60 with time axis respectively as Sown beiow The ratio of two velorities is (1) (3) 2

Under absorption costing, a company can wait to recognize fixed costs as expense simply by selling more than they produced that period. Select one: True False

Question No. one: Multiple Choice (20 Malks) 1- *Moderating year-to-year fluctuations in income by shifting earnings from peak years to less successful periods is: A) Income smoothing, B) Quality of...