Question: Let t: P2 P2 be a0 + a1x + a2x2 (5a0 + 6a1 + 2a2) - (a1 + 8a2)x + (a0 - 2a2)x2

Let t: P2 → P2 be
a0 + a1x + a2x2 → (5a0 + 6a1 + 2a2) - (a1 + 8a2)x + (a0 - 2a2)x2∙
Find its eigenvalues and the associated eigenvectors.

Step by Step Solution

★★★★★

3.33 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

With respect to the natural basis B 1 x x 2 the matrix representation is this Thus the characterist... 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

961-M-L-A-L-S (5759).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let T: P2 P2 be define by T(a0 + a1x + a2x2) = (5a0 + 6a1 + 2a2) - (a1 + 8a2)x + (a0 - 2a2)x2 (a) Find the eigenvalues of T. (b) Find bases for the eigenspaces of T.

Q:

Let T: P2 P3 be the transformation that maps a polynomial p(f) into the polynomial (t + 3)p(f). a. Find the image of p(f) = 3 - 2t C t2. b. Show that T is a linear transformation. c. Find the matrix...

Q:

Let T: P2 P4 be the transformation that maps a polynomial p(t) into the polynomial p(t) C 2t2p(t). a. Find the image of p(t) = 3 - 2t C t2. b. Show that T is a linear transformation. c. Find the...

Q:

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...

Q:

8.4 Write on paper for upvote please. Questions: 12, 17, 22 8.4 Matrices for General Linear Transformations 485 b. Verify that Formula (8) holds for every vector in R'. d. Use the formula obtained in...

Q:

8.1 WRITE on paper for upvote. Section: 25, 32, 33 please 8.1 General Linear Transformations 20. Consider the basis S = {V1, V2} for R', where v, = (-2, 1) and 9. T : Rx - R., where V2 = (1, 3), and...

Q:

Consider a system employing a deadlock - avoidance scheme based on pre - declaration of resource needs for various processes. In particular, the resource needs of the processes are represented by...

Q:

Math 110, Fall 2015. Homework 6, due Oct 7. Prob 1. Let V = P2 (IR) and suppose j (p) = p(j), j = 0, 1, 2. Prove that (0 , 1 , 2 ) is a basis for P2 (IR) and nd a basis (p0 , p1 , p2 ) of P2 (IR)...

Q:

Adams and Yellen (1976) A firm is selling good 1 and good 2. Pat wants to purchase at most one of each object, and has valuation v for good 1, v2 for good 2, and v + v2 for both. If Pat purchases...

Q:

(4) Does the line Li which passes through (1, 1, 4) and (3, 3, 2) intersect L2, the line through (-1, -1,3) and (4, 4, 7)? Justify your answer. 1 +t (5) Find the point Q on the line L(t) = t which is...

Q:

A uranium oxalate actinometer is irradiated for 15 min with 4350 A light. At the end of this period it is found that the oxalic acid corresponding to 12 cm 3 of KMnO4 at 0.001 M has been decomposed...

Q:

29. LO.1 Perk Corporation is subject to tax only in State A. Perk generated the following income and deductions. Federal taxable income $300,000 State A income tax expense 15,000 Refund of State A...

Q:

Duration Analysis Gauss file(s) qmle_exponential.g Matlab file(s) qmle_exponential.m The true model of duration times between significant events follows an exponential distribution with parameter 0....

Q:

Let A be a diagonalizable matrix with characteristic polynomial (a) If D is a diagonal matrix whose diagonal entries are the eigenvalues of A, show that = p(D) + a1Dn + a2Dn-1 + an+1I = 0 (b) Show...

Q:

For each of the following, find a matrix B such that B2 = A. a. b. 2 9 -5 3 A =10 4 3 0 0 1

Q:

Let A be a nondefective n x n matrix with diagonalizing matrix X. Show that the matrix Y = (X-1)T diagonalizes AT.

Q:

I would like some direction into gathering the data needed for this problem. I don't need the answer but rather what type of analysis would you recommend? FCF? Walgreen was planning to buy Rite-Aid...

Q:

You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $1.850 and you have made every payment on time. The...

Q:

I need help filling out this ProForma. Please show the formulas used. Thanks. G H I K L M N 0 Year 3 Year 4 Year 5 % % % Per Door % % * Per Door % Per Door A B D E F 1 Independent Variables for Hotel...