Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 9.2, Problem 12E
Determine the stability of the system
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Co Given
show that
Solution
Take home
Су-15
1994
+19
09/2
4
=a
log
суто
-
1092
ж
= a-1
2+1+8
AI | SHOT ON S4
INFINIX CAMERA
a
Question 7. If det d e f
ghi
V3
= 2. Find det
-1
2
Question 8. Let A = 1
4
5
0
3
2.
1 Find adj (A)
2 Find det (A)
3
Find A-1
2g 2h 2i
-e-f
-d
273
2a 2b 2c
Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 9 Solutions
Linear Algebra with Applications (2-Download)
Ch. 9.1 - Solve the initial value problems posed in...Ch. 9.1 - Solve the initial value problems posed in...Ch. 9.1 - Solve the initial value problems posed in...Ch. 9.1 - Solve the initial value problems posed in...Ch. 9.1 - Solve the initial value problems posed in...Ch. 9.1 - Solve the nonlinear differential equations in...Ch. 9.1 - Solve the nonlinear differential equations in...Ch. 9.1 - Solve the nonlinear differential equations in...Ch. 9.1 - Solve the nonlinear differential equations in...Ch. 9.1 - Solve the nonlinear differential equations in...
Ch. 9.1 - Solve the nonlinear differential equations in...Ch. 9.1 - Find a differential equation of the form dx/dt=kx...Ch. 9.1 - In 1778, a wealthy Pennsylvanian merchant named...Ch. 9.1 - The carbon in living matter contains a minute...Ch. 9.1 - Justify the “Rule of 69”: If a quantity grows at a...Ch. 9.1 - For the values of1and2given in Exercises 16...Ch. 9.1 - For the values of1and2given in Exercises 16...Ch. 9.1 - For the values of1and2given in Exercises 16...Ch. 9.1 - For the values of1and2given in Exercises 16...Ch. 9.1 - Consider the system dx/dt=Axwith A=[0110] . Sketch...Ch. 9.1 - Consider the system dx/dt=Axwith A=[0100] . Sketch...Ch. 9.1 - Consider the linear system dx/dt=Ax of arbitrary...Ch. 9.1 - Consider the linear system dx/dt=Ax of arbitrary...Ch. 9.1 - Let A be an nn matrix and k a scalar. Consider the...Ch. 9.1 - Let A be an nn matrix and k a scalar. Consider the...Ch. 9.1 - In Exercises 26 through 31, solve the system with...Ch. 9.1 - In Exercises 26 through 31, solve the system with...Ch. 9.1 - In Exercises 26 through 31, solve the system with...Ch. 9.1 - In Exercises 26 through 31, solve the system with...Ch. 9.1 - In Exercises 26 through 31, solve the system with...Ch. 9.1 - In Exercises 26 through 31, solve the system with...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Sketch rough phase portraits for the dynamical...Ch. 9.1 - Find a 22 matrix A such that the system dx/dt=Ax...Ch. 9.1 - Consider a noninvertible 22 matrix A with two...Ch. 9.1 - Consider the interaction of two species of animals...Ch. 9.1 - Answer the questions posed in Exercise 42 for the...Ch. 9.1 - Answer the questions posed in Exercise 42 for the...Ch. 9.1 - Two herds of vicious animals are fighting each...Ch. 9.1 - Repeat Exercise 45 for the system | dx dt=py dy...Ch. 9.1 - The interaction of two populations of animals is...Ch. 9.1 - Repeat Exercise 47 for the system | dx dt=x+ky dy...Ch. 9.1 - Here is a continuous model of a person’s glucose...Ch. 9.1 - Consider a linear system dx/dt=Ax , where A is a...Ch. 9.1 - Let x(t) be a differentiable curve in n and S an...Ch. 9.1 - Find all solutions of the system dxdt=|10|x where ...Ch. 9.1 - Solve the initial value problem dxdt=|pqqp|x with...Ch. 9.1 - Consider a door that opens to only one side (as...Ch. 9.1 - Answer the questions posed in Exercise 54 for the...Ch. 9.2 - Use the definition of the complexvalued...Ch. 9.2 - Use the definition of the complexvalued...Ch. 9.2 - Use the definition of the complexvalued...Ch. 9.2 - Sketch the trajectory of the complexvalued...Ch. 9.2 - Sketch the trajectory of the complexvalued...Ch. 9.2 - Find all complex solutions of the system...Ch. 9.2 - Determine the stability of the system dxdt=[1234]xCh. 9.2 - Consider a sytem dxdt=Ax where A is a symmetric...Ch. 9.2 - Consider a sytem dxdt=Ax where A is a 22 matrix...Ch. 9.2 - Consider a quadratic form q(x)=xAx of two...Ch. 9.2 - Do parts a and d of Exercise 10 for a quadratic...Ch. 9.2 - Determine the stability of the system...Ch. 9.2 - If the system dx/dt=Ax is stable, is dx/dt=A1x...Ch. 9.2 - NegativeFeedbackLoops. Suppose some quantities...Ch. 9.2 - Consider a noninvertible 22 matrix A with a...Ch. 9.2 - Consider the system dxdt=[01ab]x where a and b are...Ch. 9.2 - Consider the system dxdt=[0kk1]x where k is an...Ch. 9.2 - Consider a diagonalizable 33 matrix A such that...Ch. 9.2 - True or False? If the trace and the determinant of...Ch. 9.2 - Consider a 22 matrix A with eigenvalues i . Let +i...Ch. 9.2 - Ngozi opens a bank account with an initial balance...Ch. 9.2 - Find each of the linear systems in Exercises 22...Ch. 9.2 - Find each of the linear systems in Exercises 22...Ch. 9.2 - Find each of the linear systems in Exercises 22...Ch. 9.2 - Find each of the linear systems in Exercises 22...Ch. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.3 - Find all real solutions of the differential...Ch. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Find all real solutions of the differential...Ch. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - The displacement of a certain forced oscillator...Ch. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Question 5. Let A, B, C ben x n-matrices, S is nonsigular. If A = S-1 BS, show that det (A) = det (B) Question 6. For what values of k is the matrix A = (2- k -1 -1 2) singular? karrow_forward1 4 5 Question 3. Find A-1 (if exists), where A = -3 -1 -2 2 3 4 Question 4. State 4 equivalent conditions for a matrix A to be nonsingulararrow_forwardHow long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)arrow_forward
- Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w karrow_forwardConsider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]arrow_forwardQuestion 4 Find the value of the first element for the first row of the inverse matrix of matrix B. 3 Not yet answered B = Marked out of 5.00 · (³ ;) Flag question 7 [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places] Answer:arrow_forward
- Question 2 Not yet answered Multiply the following Matrices together: [77-4 A = 36 Marked out of -5 -5 5.00 B = 3 5 Flag question -6 -7 ABarrow_forwardAssume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the abovearrow_forwardSelect the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forward
- Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY