Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Question
Chapter 8.1, Problem 4E
To determine
To write: the given linear system in matrix form.
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5.
By using the matrix methods to solve the following linear system:
I1 + 12 – 13 = 5, 3r1 +x2 – 2r3 = -4,
-I1 + 12 - 2r3 = 3;
2
5 31
5. Write X =|-3 6 0 as the sum of a skew symmetric and a symmetric
4
1 1]
matrix.
9. (a) Evaluate the matrix product Ax, where
A =
1.
and x =
3
Hence show that the system of linear equations
7x + 5y = 3
x + 3y = 2
can be written as Ax
b where b =
%3D
(b) The
system
of equations
2r + 3y – 2z = 6
x– y + 2z = 3
4x + 2y + 5z = 1
can be expressed in the form Ax = b. Write down the matrices A, x and b.
Chapter 8 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - Prob. 8ECh. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 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. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - In Problem 27 of Exercises 4.9 you were asked to...Ch. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 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 - In Problems 3546 find the general solution of the...Ch. 8.2 - Prob. 46ECh. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - Prob. 48ECh. 8.2 - The system of mixing tanks shown in Figure 8.2.7...Ch. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 53ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Consider the large mixing tanks shown in Figure...Ch. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - The system of differential equations for the...Ch. 8.3 - Prob. 36ECh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - In problem 58 use (1) use to find the general...Ch. 8.4 - In problem 58 use (1) use to find the general...Ch. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 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 - Prob. 26ECh. 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 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RE
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- 3. Q1: Given A = -1 4 3 3. find the matrix X if 2xT-AB = -2 B = 1 -3arrow_forward2. 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.arrow_forwardHomogeneous Systems In Problems 53–55, determine all the solutions of Ax = 0, where the matrix shown is the RREF of the augmented matrix (A | b). ri -2 0 5 0 1 2 0 0 0 53. 0 lo 1 55. (1 - 4 3 010]arrow_forward
- 13 () 9. If A is a 3 x 3 matrix such that A 1 and A 4 1 then the product A 7 is %3D %3D 8arrow_forwardProblem 8. Determine whether the 2×2 matrix (1) is in the span of {(18), (11),(18)}. 1arrow_forwardHELP 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_forward
- 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 = 9arrow_forward3. Let A be a 4 × 4 matrix. Suppose the matrix equation A = has solution set 1 what is the solution set of A = 0? 2.arrow_forwardFind the value of x if the matrix 1 5 4 is Singular 2 x. 6.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_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_forwardProblems 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_forward
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