Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter B, Problem 36E
To determine
To solve: The given equation by Gaussian elimination method.
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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;
In Problems 39–43, solve each system of equations.
Į 2r + y + 3 = 0
x² + y? = 5
x + y? = 6y
x = 3y
S2xy + y? = 10
39.
40.
41.
| 3y² – xy = 2
Ј Зx? + 4ху + 5у? 3D 8
42.
x² - 3x + y² + y = -2
43.
lx² + 3xy + 2y² = 0
+ y + 1 = 0
y
4.
Use the Gauss-Siedel method to approximate the solution of the following system of linear
equations. (Hint: you can stop iteration when you get very close results in three decimal
places.)
5х1 — 2х2 + 3хз
= -1
— 3х1 + 9х2 + хз — 2
2x1 – x2 – 7x3 = 3
Chapter B Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. B - Prob. 1ECh. B - Prob. 2ECh. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - In Problems 1522 determine whether the given...Ch. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Prob. 20ECh. B - Prob. 21ECh. B - In Problems 1522 determine whether the given...Ch. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50ECh. B - Prob. 51ECh. B - Prob. 52ECh. B - Prob. 53ECh. B - Prob. 54ECh. B - Prob. 55ECh. B - Prob. 56ECh. B - Prob. 57ECh. B - Prob. 58ECh. B - Prob. 59ECh. B - Prob. 60ECh. B - Prob. 61ECh. B - Prob. 62E
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- 4. (S.10). Use Gaussian elimination with backward substitution to solve the following linear system: 2.r1 + 12 – 13 = 5, 1 + 12 – 3r3 = -9, -I1 + 12 +2r3 = 9;arrow_forward8. Use any method to find the general solution of the system x + 2 [1/₂].arrow_forwardSection 2.2 2.1. Solve the following difference equations: (a) Yk+1+Yk = 2+ k, (b) Yk+1 – 2Yk k3, (c) Yk+1 – 3 (d) Yk+1 – Yk = 1/k(k+ 1), (e) Yk+1+ Yk = 1/k(k+ 1), (f) (k + 2)yk+1 – (k+1)yk = 5+ 2* – k2, (g) Yk+1+ Yk = k +2 · 3k, (h) Yk+1 Yk 0, Yk = ke*, (i) Yk+1 Bak? Yk (j) Yk+1 ayk = cos(bk), (k) Yk+1 + Yk = (-1)k, (1) - * = k. Yk+1 k+1arrow_forward
- 8. Solve the following simultaneous equations using Gaussian elimination: x – 2y + 3z 9 -x + 3y + z -2 2л — 5у + 52 17 -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_forwardSection 2.2 2.1. Solve the following difference equations: (a) Yk+1+ Yk = 2+ k, (b) Yk+1 – 2yk = k³, (с) ук+1 "Yk = 0, (d) Yk+1 – Yk = 1/k(k+1), (e) Yk+1+ Yk = 1/k(k+1), (f) (k+2)yk+1 – (k + 1)yk = 5 + 2k – k², (g) Yk+1+ Yk = k + 2 · 3k, (h) Yk+1 – Yk = ke“, Yk = Bak*, = cos (bk), (k) Yk+1 + Yk = (-1)*, Yk – k. ,2k (i) Ук+1 (j) Yk+1 – aYk (1) Yk+1 k+1arrow_forward
- 2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination process. -x1 + 3x2 – 2.x3 + 4x4 = 0 4.x1 + 12r, + 7r3 – 14x4 -1 I1 – 3r2 + 4x3 – 874 2x1 – 6x2 + x3 – 2.74 2 -3. Write the solution in column form by explicitly isolating the parameter(s) associated with free variable(s), if there is any. (b) Consider the following matrix 1 4 -1 2 7 1 -2 A = 1 0 3 -3 -5 i. Find an LU-factorization of A. ii. Use these L and U to solve the system Ax = b, where x = and I3 1 7 b = 5 (c) Find A-1. Use A-1 to solve the system Ax = b, where A, x and b are the same as given in 2(b).arrow_forward2) Find the General Solution of the System of Equations. [1 0 0] X' = 2 1 -2 X 3 2 1arrow_forward5. How many solutions does the system y = 3x? and y = 7x + 6 have? [A] 1 (B] 2 [C13 [D]4arrow_forward
- 2. Use Gauss elimination with back substitution to solve the system of linear equations: &x, +x2 +4x3 +8x, = 5 x1 - 7x, – 2x, – 7x4 : 1 7x, - 2x2 + 7x3 +2x4 =-5 X1 +x, +2x3 – 6x, = -5 Round-off to 5 significant figures.arrow_forward14 What is the solution to the system of m of 2x ty-Z = 5 F (4, 1, 4) X+32 =14 (-1, 12, 5) н (3, 0, 4) -2x -3y + 22 = 2 (5,-2,3)arrow_forwardIn Exercises 15–16, solve each system using matrices. 15. (2x + y = 6 13x – 2y = 16 x - 4y + 4z = -1 2х — у + 52 16. -x + 3y - z =arrow_forward
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