Please answer question 4 1. Consider the matrices4A₁ = - (13) 42-(3-2)023-2).These matrices can be used to build functions x¹A₁x, x¹ A₂x, x¹ A3x, and x¹ A4x. These functionsare represented (in an arbitrary order) in Figure 1. Match each matrix with its corresponding picture.=Explain briefly.2. Consider matrices of the form(a) Ma, ≥ 0.(b) Ma,B ≤ 0.3. Is the matrixMa,ß = a0(b)(c)Figure 1: Graphical representation of functions, A3 =1-a001 -2α ( -2 -² ) + ³ ( -1 -₂ )2-2where a and 3 are scalars. Depending on the values of a and 3, these matrices might be psd, nsd, orindefinite. In a graph with axes a and 3, represent the set of all (a, 3) values for which the matrix5-41psd, pd, nsd, nd, or indefinite? Justify your answer.4. Consider the matrix"15 -14and A4 =-5-400-a0-2a(a² + a)0- (2-a²)(2-a²)(2-a²) 2+ 4a - a²-2aFind all values of a for which this matrix is psd. Are there values of a for which the matrix is pd?ə

4) Solution:According to the given data, find the all values of a for which given matrix is psd.

Answered: 4. Consider the matrix 1 0 0 0 0 0 -2a…

4. Consider the matrix 1 0 0 0 0 0 -2a -a (a² + a) 0 (2-a²) - (2-a²) -2a (2-a²) 2+ 4a - a² Find all values of a for which this matrix is psd. Are there values of a for which the matrix is pd?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 40EQ

See similar textbooks

Related questions

Q: find the general solution by finding the homogeneous solution and a particular solution.

A: 17. Given that the differential equation is To find…

Q: B.C. IC. Solve completely to the final form of the solution as a Fourier Series the heat equation…

A: Using seperation of variables method:Let u(x,t)=X(x)T(t)From the conditions :u(0,t)=u(1,t)⇒…

Q: 3.2: Markov Chains are Proper Probabilistic Models Show that the sum of the probabilities over all…

A: To show that the sum of the probabilities over all possible sequences of any length is 1, which…

Q: 6. 7. Which of the following functions has the longest period? y = 6 sin(3x) + 20 b. y = 8 cos(2x) -…

Q: Which set of values for x should be tested to determine the possible zeros of 2x³ - 3x² + 3x - 10? O…

Q: Tonya's ZIP code is 24760. How many zip codes altogether could be formed, each one using those same…

Q: part d) Use T3(t) to approximate the value of d(10 + b/6 ). (Round your answer to two decimal…

A: We have to find the approximate value of the function using the function where .Here, is the third…

Q: list the days during the next 60 days on which megan and michele will see each other in city b

A: Given that:-Megan flies a 21 day schedule( including days off) which then repeats.Michele has a 30…

Q: 1. Due to the quarantine, the demand for Nine Tendo On/Off console suddenly peaked and is expected…

A: Decision variables:xq : number of units purchased in quarter q.yq : number of units held over from…

Q: Solve the initial-value problem where f(t)= = 2: y'-y = f(t), y(0) = 1 0 ≤t≤1 t≥1 1: in the…

Q: me table below shows the production of tobacco in the US, in millions of pounds.¹ Year Year 2006…

A: (a) The average rate of change in tobacco production between 2008 and 2019 ismillions of pounds per…

Q: Show that translations are commutative. That is, if matrix T(d) represents a translation by d₂…

A: To show that translations are commutative, we'll use the matrix representation of translation. Let…

Q: Find an equation of the tangent line to the curve (a lemniscate) at the point (3, -1). 2(x² + y²)² =…

Q: Find the limit lim (z,y) → (0,0) r²y¹ cos(x + y²) x² + y²

Q: Let U = {1, 2, 3, 4, 5, 6, 7}, A={2, 3, 6, 7}, and B = {3, 5, 6}. Find the set A¹ n B'. A' B'= (Use…

Q: 13. Using Newton-Raphson method solve x log10 x = 12.34 with co = = 10. O

Q: 1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n) = 5n+20 n³ - 10 n² + 10

A: To show that: P(n)=O(n4)We will use the definition of big oh notation to show this, we will find a…

Q: Question 2. Our goal is to prove that f(x) = x + e* has exactly one root (i.e. f(x) = 0 for exactly…

Q: 1. Find all solutions of the congruence 5x+3x²+x+3 = 0 mod 30.

A: The congruence .To Find:Solution of the above congruence.

Q: An office tenant needs 3,550sf of usable space in which to operate their business. If they locate in…

Q: Exercise 6.1.14: Find the Laplace transform of sin(w(t – a)).

A: We have to find the Laplace transformation of the given function

Q: Consider a dynamical system given by the transformation T:[0,1)→[0,1) defined as: This is known as…

A: Birkhoff's Ergodic Theorem states that for almost every point x in our space and for any integrable…

Q: f(x) = x + 1, g(x) = 2x + 1, h(x) = 3x + 1, then are the functions f, g, and h linearly independent…

A: Let the function be .To Find:Are the functions linearly independent?

Q: Question 2. Find the limit lim (x,y) (0,0) 2¹+ y² + ys

A: Q2: we have to find out if exists.we claim that Now using A.MG.M , so we get ,but So we get Now…

Q: For a certain company, the cost for producing items is 55x + 300 and the revenue for selling x items…

A: Let us solve above problem

Q: . Find the general solution of dy d.x = 2 y + 1 x+y-2 2

A: Given differential equation isdy/dx = 2 ((y+1)/(x+y-2))2

Q: A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128/257…

A: Given information:A steel ball weighs .The ball is suspended from a spring, stretching it by .The…

Q: 2. Sketch a graph of r = 1 - sin 0 and r = 1 on the polar coordinate system provided below. Assume 0…

Q: 0 X e-x/y y dx

Q: What value of x that will make the equation In x +=(x-2)² true using Newton-Raphson method with an…

A: Newton Raphson Method:-Here we consider initial value x0 =e=2.718182 and.

Q: how to simplify (ANB)U(ANB)U(A'NB')?

Q: Determine the value of the parameter t for which the following system has a unique solution and…

Q: Sketch the region enclosed by 2y = 3√x, y = 3, and 2y + 3x = 6. Decide whether to integrate with…

Q: c. sin 2x = 2 tan x 1+tan² x d. 2 cos x cos 2x+1 = sec x

Q: Solve ONE of the following problems using a modern method: . Approximate √31 to six decimal places.…

Q: If F = {0, 1, x} is a field with three elements, then (x + 1) + x is equal to

A: Given that is a field.Then is abelian group under addition and is abelian group under…

Q: (c) Find the limit of Σ r=N+l N (3r+1)(3r-2) as N →∞0.

Q: a) 11001 / (01011 v 11010) b) (01011 10101) + 01010

Q: 5 4 3 2 Us The graph of a function y = f(x) is shown. Make a sketch of the antiderivative F, given…

Q: 11. a) U₁₁ A₁ Let A₁ = {i,i+1,i+2,...} for i=1,2,3,.... Find b) Ai

Q: 4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) =…

Q: Let R4 have the Euclidean inner product. Find a unit vector with a positive first component that is…

Q: For the following sequence, determine if it is an arithmetic sequence, a geometric sequence, or…

Q: For the system of differential equations (D+1)x + (D-1)y = 2 3x + (D+2)y = -1 solution for y(t). 9.…

Q: The entire graph of the function h is shown in the figure below. Write the domain and range of h…

A: The domain is the collection of points where the function is defined. For this, we need to check the…

Q: Consider the following indefinite integral. The integrand decomposes into the form: Compute the…

Q: Please use the Laplace transform. I only need help with part c

Q: If A is a 4 x 2 matrix, what are the possible values of nullity(A)? (Enter your answers as a…

A: The nullity of a matrix A is the dimension of the null space of A, which is also known as the kernel…

Q: Draw a graph off that satisfies the given specifications for the domain [-3, 3]. The function does…

A: We need to find the graph from given options.

Q: Use the eighteen rules of inference to derive the conclusions of the symbolized argument below. Q S…

Question

Please answer question 4

1. Consider the matrices
4
A₁ = - (13) 42-(3-2)
0
23-2).
These matrices can be used to build functions x¹A₁x, x¹ A₂x, x¹ A3x, and x¹ A4x. These functions
are represented (in an arbitrary order) in Figure 1. Match each matrix with its corresponding picture.
=
Explain briefly.
2. Consider matrices of the form
(a) Ma, ≥ 0.
(b) Ma,B ≤ 0.
3. Is the matrix
Ma,ß = a
0
(b)
(c)
Figure 1: Graphical representation of functions
, A3 =
1
-a
0
0
1 -2
α ( -2 -² ) + ³ ( -1 -₂ )
2
-2
where a and 3 are scalars. Depending on the values of a and 3, these matrices might be psd, nsd, or
indefinite. In a graph with axes a and 3, represent the set of all (a, 3) values for which the matrix
5
-4
1
psd, pd, nsd, nd, or indefinite? Justify your answer.
4. Consider the matrix
"
1
5 -1
4
and A4 =
-5
-4
0
0
-a
0
-2a
(a² + a)
0
- (2-a²)
(2-a²)
(2-a²) 2+ 4a - a²
-2a
Find all values of a for which this matrix is psd. Are there values of a for which the matrix is pd?
ə

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given:

VIEW

Step 2: Now calculate det and trace:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here