Question: Let A be a square matrix. (a) Suppose that the homogeneous system Ax = 0 has a nontrivial solution x = u. Show that u

Let A be a square matrix.
(a) Suppose that the homogeneous system Ax = 0 has a nontrivial solution x = u. Show that u is an eigenvector of A?
(b) Suppose that 0 is an eigenvalue of A and v is an associated eigenvector. Show that the homogeneous system Ax = 0 has a nontrivial solution?

Step by Step Solution

★★★★★

3.48 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Since Au 0 0u it follows that 0 ... 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)

951-M-L-A-L-S (7137).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let A be a square matrix that can be partitioned as where P and S are square matrices. Such a matrix is said to be in block (upper) triangular form. Prove that det A = (det P)(det S) o S

Let U be an upper triangular matrix. Show that the homogeneous system U x = 0 admits a nontrivial solution if and only if U has at least one 0 on its diagonal.

Let X1 and X2 be solutions to the homogeneous system AX = 0. Show that tX1 is a solution to AX = 0 for any scalar t.

1 1. (6+4+4+6) Let P3 denote the vector space of all third degree or less polynomials. (a) Find two linearly independent vectors in P3 that interpolate the data points (1, 2), (2, 1) and (3, 2). (b)...

using MATLAB write s code that SOLVING HOMOGENEOUS SYSTEMS EXERCISE 5 (5 points) Difficulty: Hard Theory: In this exercise, you will work with the solution set of a homogeneous linear system Ax = 0,...

SOLVING HOMOGENEOUS SYSTEMS EXERCISE 5 (5 points) Difficulty: Hard Theory: In this exercise, you will work with the solution set of a homogeneous linear system Ax=0, where A is an mxn matrix and...

PDF Reader X 230prac1f20.pdf X + . .. Enter Search Text ? BOTA 1 / 1 55% Q E X Math 2300 Practice Problems 1. Deternine the solutions to the linear system cty+z=1 -2x - 42 = 4 y - z = 3 How is your...

1. (2points each). Answer each of the following as true or false. a) If A and B are n x n matrices, then (A + B)(A + B) = A2 + 2AB + 82. b) If u and uz are solutions to the linear system Ax = b, then...

What particular strengths of the relational model have led to the pre-eminent position that it holds today as a vehicle for database management? [8 marks] Identify any weaknesses in the model,...

In response to the weak economy, your companys sales force is urging you, the sales manager, to change sales terms from 1/10, n/30 to 2/10, n/45. Explain what these terms mean and how this switch...

Suppose a randomly selected passenger is about to go through the metal detector at JFK Airport in New York City. Consider the following two outcomes: The passenger sets off the metal detector, and...

How can the effectiveness of a salesforce be assessed?

You are the project manager of the NHQ Project. Your project team consists of experts from different departments within your organization. What type of organizational structure is this? A. Virtual B....

Make a hand-drawn graph. Be sure to label all the asymptotes. List the domain and the x-intercepts and the y-intercepts. Check your work using a graphing calculator? a. b. c. f(x) = x h(x) =-4

Use your knowledge of asymptotes and intercepts to match the equation with one of the graphs (a)-(f), which follow. List all asymptotes. Check your work using a graphing calculator. a) b) c) a) b) JL...

Find a rational function that satisfies the given conditions, Answer may very, but try to give the simplest answer possible. a. Vertical asymptotes x = - 4, x = 5 b. Vertical asymptotes x = - 4, x =...

QUESTION 1 One year ago, you purchased 300 shares of Southern Cotton at $32.60 a share. During the past year, you received a total of $280 in dividends. Today, you sold your shares for $35.80 a...

The following data are the returns for 1980 through 1986 on five types of capital-market instruments: common stocks, small-capitilzation stocks, long-term corporate bonds, long-term U.S. government...

The internal rate of return (IRR) refers to the compound annual rate of return that a project generates based on its up-front cost and subsequent cash flows. Consider this case: Blue Llama Mining...