Question: In each case, compute the characteristic polynomial cT(x). (a) T : R2 R2, T(a, b) = (a - b, 2b - a) (b) T:

In each case, compute the characteristic polynomial cT(x).
(a) T : R2 †’ R2, T(a, b) = (a - b, 2b - a)
(b) T: R2 †’ R2, T(a, b) = (3a + 5b, 2a + 3b)
(c) T: P2 †’ P2, T(a + bx + cx2) = (a - 2c)
+ (2a + b + c)x + (c - a).x2
(d) T: P2 †’ P2, T(a + bx + cx2) = {a + b - 2e)
+ (a- 2b + r)x + {b - 2a)x2
(e) T: R3 †’ R3, T(a, b, c) = (b, c, a)
(f)

T M2>M22.1:1H:3 ::/

Step by Step Solution

★★★★★

3.33 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

b Choose a basis of R 2 say B 1 0 0 1 and compute M B T C B T1 0 C B T0 1 C ... View full answer

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)

950-M-L-A-L-S (6669).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

For each value of a in the set {32, 31.9, 31.8, 32.1,32.2}, compute the characteristic polynomial of A and the eigenvalues. In each case, create a graph of the characteristic polynomial p(t) = det (A...

The characteristic polynomial of the square matrix A is usually defined as rA(x) = det (xIn - A). Find a specific relationship between our characteristic polynomial, pA (x), and rA(x), give a proof...

Consider the matrices Note that the two matrices are the same except for their (2, 2) entries. (a) Use MATLAB to compute the eigenvalues of A and B. Do they have the same type of eigenvalues? The...

SOLVE Questions 1-5: PLEASE AND THANK YOU 1: What is the difference between homogenous and non-homogenous differential equation? Write an example for each and solve it. 2: What is the main formula to...

\f\f3. a) potential function = x2 +y 2 +z 2 ; magnetic force M = y 2 zi+z 2 xj+x2 yk i) Grad = i+ j+ k x y z Note that : = 2x = 2y = 2z x y z Hence, Grad = 2xi + 2yj + 2zk M M M ii) Div M = + + x y z...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

calculate below questions and provide easy step format thankyou. (1) Consider the following system of linear equations, ax - 2y +2 = I + ay + 2z = a where a E R is a parameter. (a) Classify the above...

Question 4 (15 p) Assume that national income, Y, is exogenously set at one fixed level (full employment) in both the short-run and in the long-run, and that the exchange rate is floating. Assume...

Find a basis for the eigenspace corresponding to the eigenvalue. - 12 J A = 14 ,2=3 3 -39 A basis for the eigenspace corresponding to 2 = 3 is {} (Type a vector or list of vectors. Type an integer or...

Consider the regression model Yt = 0 + 1Xt + ut, where ut follows the stationary AR(1) model with mean 0 and variance a. Suppose that Xt is independent of uj for all t and j. Is Xt exogenous (past...

A critic of Canada Post claims that its financial returns are typically $200 million less than forecast. In five of the years of the 1990s, the mean difference (in millions of dollars) between Canada...

The diversifiable risk includes the risk due to . . . . . Question 2 4 Answer a . Industrial recession or slow down. b . Inflation c . Natural calamities d . Strike in the company

Benzaquin had a radio talk show in Boston. On the program, he complained about an incident earlier in the day, in which state trooper Fleming had stopped his car, appar ently for lack of a proper...

Show that none of the following matrices is diagonalizable: (a) (b) (c) (d) 005 230 10113- -34-3 L-8-8-1 5311 3210 3200 -2 300

Let L: P1 P1 be the linear operator defined by L(at + b) = -bt - a. Find, if possible, a basis for P1 with respect to which L is represented by a diagonal matrix?

Let A and B be nonsingular n ( n matrices. Prove that AB and BA have the same eigenvalues?

Valuation is the analytical process of establishing the worth of an asset or a business. There are many techniques used for doing a valuation. We look at two: stock valuation and bond valuation.\ \...

I need help with these questions Suppose that over a certain region of space the electrical potential V is given by V(x. y. 2) = 7r - Ary + ryz. Find the rate of change of the potential at P(1. 3, 7)...

Week 9 * Question Completion Status: Week 10 Week 11 Which of the following are characteristics of the normal distribution O A. It is bell-shaped Week 12 O B. It extends indefinitely in each...