Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 9, Problem 7P
Given the equations
(a) Solve graphically.
(b) Compute the determinant.
(c) On the basis of (a) and (b), what would you expect regarding the system's condition?
(d) Solve by the elimination of unknowns.
(e) Solve again, but with
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-2 4 6
. Solve for the determinant of
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Consider the following pair of simultaneous equations:
6x + 4y − 14 = 0
5x − 3y − 37 = 0
(b) Solve the above equations using determinants.
Solve for x.
|x+3x1 = 0
4
STEP 1: Solve for the determinant in terms of x.
31-
x+3
4 x-1
STEP 2: Set your result from Step 1 equal to zero and solve for x.
x =
Chapter 9 Solutions
Numerical Methods for Engineers
Ch. 9 - (a) Write the following set of equations in matrix...Ch. 9 - A number of matrices are defined as...Ch. 9 - Three matrices are defined as...Ch. 9 - Use the graphical method to solve...Ch. 9 - 9.5 Given the system of equations
(a) Solve...Ch. 9 - 9.6 For the set of equations
(a) Compute the...Ch. 9 - Given the equations 0.5x1x2=9.51.02x12x2=18.8 (a)...Ch. 9 - Given the equations...Ch. 9 - Use Gauss elimination to solve:...Ch. 9 - Given the system of equations...
Ch. 9 - 9.11 Given the equations
(a) Solve by Gauss...Ch. 9 - Use Gauss-Jordan elimination to solve:...Ch. 9 - 9.13 Solve:
with (a) naive Gauss elimination,...Ch. 9 - 9.14 Perform the same computation as in Example...Ch. 9 - 9.15 Solve
Ch. 9 - 9.16 Develop, debug, and test a program in either...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - 9.19 Three masses are suspended vertically by a...Ch. 9 - 9.20 Develop, debug, and test a program in either...Ch. 9 - 9.21 Recall from Sec. 8.2 that determining the...
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- Solve for x. |x + 3 STEP 1: Solve for the determinant in terms of x. |x + 3 -1 4 x- STEP 2: Set your result from Step 1 equal to zero and solve for x. X =arrow_forwardsolve the following system of equations, state how many solutions, if infinite express using formulas like (x, mx + b) or (my + b, y). Hint: use determinants to check the number of solutions. 1. -4x + 8y = -9 6x - 12y = 13.5 2. -4x + 8y = -9 5x - 10y = 20 3. -4x + 8y = -28 6x - 10y = 38arrow_forward(2x + y - 3z = -9 | x + 5z = 14 | −3x + 2y - z = 4). From 3 (three) equations, what is the value of the determinant z: Select one: O a. 40 O b.-80 O C. -120 O d. -40arrow_forward
- Solve for x. |x + 11 = 0 -36 x - STEP 1: Solve for the determinant in terms of x. |x + 11 1 -36 x - 1 STEP 2: Set your result from Step 1 equal to zero and solve for x. X =arrow_forward(b) Solve the below pair of simultaneous equations using determinants: 4x − 2y = 0 5x + 3y + 11 = 0arrow_forward3. Given the equations: x + y +z = 2, 3x – y – 2z = 4, 5x – 2y + 3z = -7. Solve for y by determinants.arrow_forward
- B. Given the system of equations -1.1x₁ + 10x₂ = 120 -2x₁ + 17.4x₂ = 174 (a) Solve graphically and check your results by substituting them back into the equations. (b) On the basis of the graphical solution, what do you expect re- garding the condition of the system? (c) Compute the determinant.arrow_forwardIf the determinant is equal to zero solve for x. * 3 1 (i) |-1 4 = -30 1 4 O 1 3arrow_forwardSolve using determinants 2x+2y=82x+y=2arrow_forward
- 9.5 Given the equations 0.5x,-X -9.5 1.02,-2,-18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system's condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a, modified slightly to 0.52, Interpret your results.arrow_forwardCalculate the operational determinant of the given system in order to determine how many arbitrary constants should appear in a general solution. Then attempt to solve the system explicitly so as to find such a general solution. (D²+5) x + (D² +10) y = 100 e-t (D²-5)x+D²y=0 CH Determine the operational determinant. The operational determinant is equal to 50 Based on the operational determinant, the general solution will have 0 arbitrary constants. Enter the general solution of the system below. x(t) = y(t) =arrow_forwardFind the solution to the linear system using determinants. Complete Steps 1 to 6 in order.arrow_forward
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