Question: Consider the matrix -1 2 - 2 2 (a) Show that the matrix B is diagonalizable. (b) Find the eigenvectors of B. (C) Find

Consider the matrix -1 2 - 2 2 (a) Show that the

Consider the matrix -1 2 - 2 2 (a) Show that the matrix B is diagonalizable. (b) Find the eigenvectors of B. (C) Find an invertible matrix P and a diagonal matrix D such that P 1AP = D Justify all your answers. 3)

Step by Step Solution

★★★★★

3.48 Rating (155 Votes )

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!

Show that a diagonal matrix is invertible if and only if all the main diagonal entries are nonzero. Describe the inverse.

find an invertible matrix P and a matrix C of the form such that A = PCP -1 . Sketch the first six points of the trajectory for the dynamical system and classify the origin as a spiral attractor,...

Find an invertible matrix P and a matrix C of the form such that A = PCP -1 . Sketch the first six points of the trajectory for the dynamical system and classify the origin as a spiral attractor,...

What does viscosity mean in terms of 3D printing and what defects can occur if this not adequately controlled.

Page 3 of 5 2 2 (20pts) 3. Consider the matrix A = 2 2 . It is given that the eigenvalues of A are -1 and 5. 2 (a) (5 pts) Find a basis for the eigenspace corresponding to each eigenvalue of A. (b)...

How to solve these 3 questions? 1. (3 marks) Consider the matrix 1 2 3 2 8 M = 0 1 3 2 8 2 1 9 4 22 i) The rank(M) and nullity(M )are given by m\"... Sam M... :m ii) Find a non-zero vector in the...

i. . , 3 5 1 Consider the matrix A = ( 2 4 ) . (a) The matrix exponential em can be written as the power series 22:0 Mtlk. Calculate the partial sums SM = 2:10 [2:'l)k for M = 1,2, 3,4. Your answers...

3. Consider the matrix A = 2 12 2 . It is given that the eigenvalues of A are -1 and 5. (a) (5 pts) Find a basis for the eigenspace corresponding to each eigenvalue of A. (b) (10 pts) Orthogonally...

Hello, i will like help with this assignment. please use details and thank you 1. Suppose that f is a function whose domain is R and satises the following properties: 0 f(:c) = 1 whens: 2 o f(0) = 1....

Consider the following. 1 0 0 A = 5 1 601 List the eigenvalues of A and bases of the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) O....

economies of scale arise when output is maximized true or false

Whether someone is a manager or a lower-status employee, a company fines them every time they "clock in" late for work. This shared accountability is an example of ____________

Bless Ltd. purchased equipment for $80,000, with an expected salvage value of $5,000 after 8 years. Calculate the book value after 3 years using the double-declining balance method. Question 21...

Mike White is planning to save up for a trip to Europe in three years. He will need 7,605 when he is ready to make the trip. He plans to invest the same amount at the end of each of the next three...

Transaction Analysis Mead Pet Hospital, owned by R. Mead, a veterinarian, opened for business on December 1 of the current year. Using the horizontal worksheet below, record the following December...

In essay format answer the following questions about the topic "Tourette syndrome" Description of the problem / topic of investigation (review of the literature) Why this problem / topic is important...

A consulting firm has two departments, Corporate and Government. Computer support is common to both departments. The cost of computer support is $3 million. The following information is given: Number...

suppose a nickel-contaminated soil 15 cm deep contained 800 mg/kg Ni, Vegetation was planted to remove the nickel by phytoremediation. The above-ground plant parts average 1% Ni on a dry-weight bas...

Let be the matrix of T: P2 P2 with respect to the basis B = (v1, v2, v3), where v1 = 3x + 3x2, v2 = -1 + 3x + 2x2, v3 = 3 + 7x + 2x2. (a) Find [T(v1)]B, [T(v2)]B, and [T(v3)]B. (b) Find T(v1), T(v2),...

Using Theorem 11.9.2, show that there is only one linearly independent price vector for the closed economic system with exchange matrix 550

Use the inner product of Exercise 3 to find ||w|| if (a) w = (1, - i) (b) w = (3 - 4i, 0)

Here are some recently reported correlations, with interpretations drawn by journalists. Knowing just these correlations, can you come up with other possible explanations for each of these? Alcohol...

3. How Is Research Knowl edge D isu;buted? Researchers Study? a. Acad e1nic Pu blishing b. Scholarly Research b. Social Di alogue and Pu blic Policy c. Applied Research c. Com muni cation in th e...

A mental health professional with a medical degree who can prescribe medication is a _______.