Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
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Chapter 9.3, Problem 12E
To determine
To find all real solutions of given
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Assume {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 above
Select 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 above
Assume {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 above
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
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- 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
- 4. In a study of how students give directions, forty volunteers were given the task ofexplaining to another person how to reach a destination. Researchers measured thefollowing five aspects of the subjects’ direction-giving behavior:• whether a map was available or if directions were given from memory without a map,• the gender of the direction-giver,• the distances given as part of the directions,• the number of times directions such as “north” or “left” were used,• the frequency of errors in directions.a) Identify each of the variables in this study, and whether each is quantitative orqualitative. For each quantitative variable, state whether it is discrete or continuousb) Was this an observational study or an experimental study? Explain your answerarrow_forwardFind the perimeter and areaarrow_forwardAssume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the abovearrow_forward
- Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the abovearrow_forwardLet H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane. Select an Answer u = 3 1. -10 8-8 -2 ,v= 5 Select an Answer -2 u = 3 4 2. + 9 ,v= 6arrow_forwardSolve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8arrow_forward
- 5. Solve for the matrix X. (Hint: we can solve AX -1 = B whenever A is invertible) 2 3 0 Χ 2 = 3 1arrow_forwardWrite p(x) = 6+11x+6x² as a linear combination of ƒ (x) = 2+x+4x² and g(x) = 1−x+3x² and h(x)=3+2x+5x²arrow_forward3. Let M = (a) - (b) 2 −1 1 -1 2 7 4 -22 Find a basis for Col(M). Find a basis for Null(M).arrow_forward
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