Let (a) Prove that A is diagonalizable if (a d) 2 4bc 0 and is not diagonalizable if (a d) 2 4bc 0 (b) Find two examples to demonstrate that if (a b) 2 4bc 0, then A may or may not be diagonalizable b A d

Question: Let (a) Prove that A is diagonalizable if (a -d) 2 + 4bc > 0 and is not diagonalizable if (a - d) 2 +

Let

(a) Prove that A is diagonalizable if (a -d)² + 4bc > 0 and is not diagonalizable if (a - d)² + 4bc < 0.
(b) Find two examples to demonstrate that if (a - b)² + 4bc = 0, then A may or may not be diagonalizable.

b. A d

Step by Step Solution

★★★★★

3.40 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Recall Exercise 35 in Section 41 We repeat the relevant parts of its solution here a If the eigenval... 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

Students Have Also Explored These Related Linear Algebra Questions!

In Exercises 1-3, let T: V W be a linear transformation between finite-dimensional vector spaces V and W Let B and C be bases for V and W, respectively, and let A = [T] CB. 1. Show that nullity(T) =...

Let A be a diagonalizable n x n matrix. Prove that if B is any matrix that is similar to A. then B is diagonalizable.

Let H be a nonempty, closed, bounded subset of Rn. a) Suppose that f : H Rm is continuous. Prove that is finite and there exists an x0 H such that ||f(x0)|| = ||f||H. b) A sequence of functions fk: H...

1. (pg 401, #14) Orthogonally diagonalize A = giving an orthogonal matrix P and a diagonal matrix D. Show all work. 2. Answer the following : (a) Show that if A is a symmetric matrix, then so is A?....

5.2 please only write on paper. no explanation needed. Questions: 22, 26, 37, 39 on paper CHAPTER 5 Eigenvalues and Eigenvectors 19. Let Show that a. A is diagonalizable if (a - d)? + 4bc > 0. b. A...

MAT 242 Written Homework #4 5.1, 5.2, 5.A Due: November 10 Solve the following problems, showing any necessary work. 0 -1 1. [3 points] For the matrix A = -2 0 -2 2 -4 0 -4 4 2 find a basis for the...

Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix P and diagonal matrix D such that P - 'AP = D. 2 20 0 3 0 0 0 3 . . . Select the correct choice...

Show all calculations Exercise 5.1. Consider the following game-frame in strategic form, where o,,02,0; and o, are basic outcomes: Player 2 O 02 Player 1 03 OA Both players satisfy the axioms of...

I'd really appreciate if I can see the answers with full steps Assignment 3 Complete this assignment after you have finished Unit 4, and submit your work to your tutor for grading. Total points: 60...

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...

A lease with a varying rental schedule is known as a structured lease. Try structuring the Greymare Bus Lines lease to increase value to the lessee while preserving the value to the lessor. Assume...

The height (in inches) of a person Choose a variable name for the given quantity. Give two numbers that the variable can represent and two numbers that it cannot represent.

Collegiate Publishing Inc. began printing operations on March 1. Jobs 301 and 302 were completed during the month, and all costs applicable to them were recorded on the related cost sheets. Jabs 303...

In Exercise 7.37 why might it be smart to look at the variances of the two groups?

Suppose a new threshold of change, Î mg/dL, is proposed for establishing compliance. We wish to use a level of Î such that the compliance measures in Problems 5.36 and 5.38 for the...

Suppose we consider the serum vitamin E assay as a screening test for compliance with vitamin E supplementation. Participants whose change in serum vitamin E is ¥ Î mg/dL will be considered...

Plot the distribution of z-scores for smokers and nonsmokers separately. Do these distributions look normal? Do smoking and pulmonary function seem in any way related in these data?

Con el objetivo de estimar el gasto promedio diario en alimentos entre los estudiantes del\ campus, se realiz una encuesta a 80 alumnos encontrndose la siguiente informacin. La media\ encontrada en...

5GE myopenmath.com Express the confidence interval 41.5 % 1 5.2% in the form of a trilinear inequality. 1pt 91 98 0 Details Express the confidence interval (9 % , 26 % ) in the form of p + E. F % %...

Question 1 A yield curve derived from a series of yields-to-maturity on zero-coupon bonds is th Group of answer choices A. A par curve. c B. A spot curve. C. A forward curve. D. None of the above....