A First Course in Differential Equations with Modeling Applications (MindTap Course List)
11th Edition
ISBN: 9781305965720
Author: Dennis G. Zill
Publisher: Cengage Learning
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Textbook Question
Chapter 8.1, Problem 4E
In Problems 1–6 write the given linear system in matrix form.
4.
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2. Find the solution set to the following system of linear equations using Gauss-Jordan
elimination.
(2.x1 + 7x2 – 12.x3
= -9
x1 + 2x2 – 3.x3 = 0
3x1 + 5x2 – 7x3 = 3
-
Determine the rank of the coefficient matrix and the augmented matrix.
.
Solving Systems Use Gauss-Jordan reduction to transform
the augmented matrix of each system in Problems 24–36 to
RREF. Use it to discuss the solutions of the system (i.e., no
solutions, a unique solution, or infinitely many solutions).
74 +
25 - - 2
29.
x₁ + 4x₂ = 5x3 = 0
2x1x2 + 8x3 = 9
Chapter 8 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 6ECh. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 10E
Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - Prob. 12ECh. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - Prove that the general solution of the homogeneous...Ch. 8.1 - Prove that the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - Prob. 4ECh. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 1-12 find...Ch. 8.2 - In Problems 13 and 14 solve the given...Ch. 8.2 - In Problems 13 and 14 solve the given...Ch. 8.2 - In Problem 27 of Exercises 4.9 you were asked to...Ch. 8.2 - (a) Use computer software to obtain the phase...Ch. 8.2 - Find phase portraits for the systems in Problems 2...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In problem 2130 find the general solution of the...Ch. 8.2 - In problem 3132 solve the given initial-value...Ch. 8.2 - Prob. 32ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 34ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 35 46 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - 38. dxdt=4x+5ydydt=2x+6y 39. X = (4554)X 40. X =...Ch. 8.2 - Prob. 53ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 55ECh. 8.2 - Examine your phase portraits in Problem 51. Under...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 2ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 6ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 9 and 10, solve the given...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - (a) The system of differential equations for the...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 14ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 16ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 31ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 33ECh. 8.3 - In Problems 33 and 34 use (14) to solve the given...Ch. 8.3 - The system of differential equations for the...Ch. 8.3 - Prob. 36ECh. 8.4 - In problem 1 and 2 use (3) to compute eAt and...Ch. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - In problem 912 use (5) to find the general...Ch. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - Prob. 18ECh. 8.4 - Let P denote a matrix whose columns are...Ch. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - A matrix A is said to be nilpotent if there exists...Ch. 8 - fill in the blanks. 1. The vector X=k(45) is a...Ch. 8 - fill in the blanks. The vector...Ch. 8 - Consider the linear system X=(466132143)X. Without...Ch. 8 - Consider the linear system X = AX of two...Ch. 8 - In Problems 514 solve the given linear system. 5....Ch. 8 - In Problems 514 solve the given linear system. 6....Ch. 8 - In Problems 514 solve the given linear system. 7....Ch. 8 - In Problems 514 solve the given linear system. 8....Ch. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - In Problems 514 solve the given linear system. 11....Ch. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - (a) Consider the linear system X = AX of three...Ch. 8 - Prob. 16RE
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- HELP WITH 18 AND 19 In each of Problems 12–23, find AR and produce a matrix 2r such that QRA = AR. -1 4 2 3 -5 7 1 18. A = 1 -3 4 4 19. A = 0 0 0arrow_forward7. Invert the following matrix 3x – 2y = 9 -x + 3y = 3 |arrow_forwardForm a coefficient matrix for the following linear system of equations: √x + 16 y = = 11 U x + 2y = -1. [26 11] 1 -1 [161] [11] Hi 0 [1¹9]arrow_forward
- 4. Solve the following system of linear equations with the inverse of the coefficient matrix (Solving for X from AX = B). x-2y+3z = 4 x+ y+ z = 2 (a) 2x + y+ z = 3 (b) x+3y+2z =1 5y-7z =-11 2x+ y- z = 2 x+2y+3z =1 4x+ y– z = 2 2x - y+4z = 3 3x+ y+ z =17 (b) (d) x+2y- z = 2 -x- 2y+ 2z = 2arrow_forwardProblem. 14: Express the system of linear equations in matrix form. 7x – 7 y + 6 = -1 3x + 8 y – 5 = 1 læ – 8 y + 7 = 5 -1 1arrow_forward1. Write the augmented matrix for this system of equations. X- 3y + 4z = 1 1 -34 1 0 3-2 5 o -1-2 3y – 2z = 5 %3D 4x- z = -2arrow_forward
- Problems 74–77 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. 74. To graph g(x) = |x + 2| – 3, shift the graph of f(x) = \x| units 76. Solve: logs (x + 3) = 2 units and then 77. Solve the given system using matrices. number Teft/right| number up/down Зх + у + 2z %3 1 75. Find the rectangular coordinates of the point whose polar 2x – 2y + 5z = 5 x + 3y + 2z = -9 coordinates are ( 6, 3arrow_forward4. Find an equation involving g, h, k that makes the augmented matrix 1 0 -2 correspond to a consistent linear system. -4 7 9 3 -5 h -9 k стarrow_forwardSuppose that 2 3 Solve the linear system Ax = b for each of the following matrices b: 8 (b) 15 (a)arrow_forward
- a. Write the augmented matrix. 7x = 9 + 2y 2(x y) = 4 b. Write a system of linear equations represented by the augmented matrix. [1 0-8 0 1 3arrow_forwardPlease help. This problem involves finding the augmented matrix and using back substitution. Thank you.arrow_forward4. Solve the linear system of equations below via matrices showing your work in detail. X1 + X2 Хз + 3 Х4 = 1 X2 Хз 4 Х4 X1 + 2 х2 - 2 Хз — Ха %3D 4x1 + 7 x2 – 7x3 = 9arrow_forward
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