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The solution x, = and x, can be read from the resulting system. Thus, the system has a unique solution. To show that the given system of equations has an infinite number of solutions for r=2, begin by substituting r=2 into each equation, and then collect all variables terms on the left side. 3x, - 4x2 = 2x4 X1- 2x2 = 2x2 (Simplify your answers) Next, eliminate x, from the second equation. Adding times the first equation to the second equation changes the second equation to (Simplify your answers.) Interpret the resulting system of equation. Choose the correct answer below and complete the corresponding answer box(es) to complete your choice. (Simplify your answers.) O A. The first equation implies that x, and the second equation mplies that X, = Since these answers are not equal, no free variables exist. Therefore, the system has an infinite number of solutions. O B. The first equation implies that x,= but there is no equation for x, Evidently, x2 is a free variable and any value can be assigned to it. Therefore, the system has an infinite number of solutions. O C. The first equation implies that x, Since these answers are equal, a free variable exists. Therefore, the system has an infinite number of solutions. and the second equation implies that x,

The solution x, = and x, can be read from the resulting system. Thus, the system has a unique solution. To show that the given system of equations has an infinite number of solutions for r=2, begin by substituting r=2 into each equation, and then collect all variables terms on the left side. 3x, - 4x2 = 2x4 X1- 2x2 = 2x2 (Simplify your answers) Next, eliminate x, from the second equation. Adding times the first equation to the second equation changes the second equation to (Simplify your answers.) Interpret the resulting system of equation. Choose the correct answer below and complete the corresponding answer box(es) to complete your choice. (Simplify your answers.) O A. The first equation implies that x, and the second equation mplies that X, = Since these answers are not equal, no free variables exist. Therefore, the system has an infinite number of solutions. O B. The first equation implies that x,= but there is no equation for x, Evidently, x2 is a free variable and any value can be assigned to it. Therefore, the system has an infinite number of solutions. O C. The first equation implies that x, Since these answers are equal, a free variable exists. Therefore, the system has an infinite number of solutions. and the second equation implies that x,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Usc tle GRUSS-Jordan elimination nlgorithrri to show that the following systom eof equations hasa unique solut'on for r= J, bul an infinito number of selutions or-2 3x, 4x - IX X1 - 2x2 - IX To show that the given system of equatiuris has A unique scluticon for r= 3, begin by substituting -3 into each caualion, and then colle:lal varisbles tcns unt the left side 3x, - 4x, - 3x, X, - 2x, - 3x2 (Siriplify your answcrs.) Swap the ruws so that the cocficiuil of x, in the first equalion hes an appropriatc valuu. The next stepin applying the Gauss-lordan climinatiori algorithm is to add a multiple ol he - eguntion to thu V equation in order to climinale Perform the stop described above Choosc the correct answer below and complete the corresponding aiswer boxes to complete your choice. (Sirrmplify your answers.) O A. Adding timos the sucund equation to the tirst cquatioI changes ihe first equation to F0 O B. Adding timos the fiest equation to the second equation chariyes lhe second equation to -0 The solution x, = and x, = can bo read lrom the resulting system. Thus, the system nas a un que solulion. To show thai the given system of equations has an infinite number of soluions Tot =2, gin by subsitutirig i=2 into sach equation, and then collect ali vanables terms on tie left sde. 3x1- 4x;
Transcribed Image Text:Usc tle GRUSS-Jordan elimination nlgorithrri to show that the following systom eof equations hasa unique solut'on for r= J, bul an infinito number of selutions or-2 3x, 4x - IX X1 - 2x2 - IX To show that the given system of equatiuris has A unique scluticon for r= 3, begin by substituting -3 into each caualion, and then colle:lal varisbles tcns unt the left side 3x, - 4x, - 3x, X, - 2x, - 3x2 (Siriplify your answcrs.) Swap the ruws so that the cocficiuil of x, in the first equalion hes an appropriatc valuu. The next stepin applying the Gauss-lordan climinatiori algorithm is to add a multiple ol he - eguntion to thu V equation in order to climinale Perform the stop described above Choosc the correct answer below and complete the corresponding aiswer boxes to complete your choice. (Sirrmplify your answers.) O A. Adding timos the sucund equation to the tirst cquatioI changes ihe first equation to F0 O B. Adding timos the fiest equation to the second equation chariyes lhe second equation to -0 The solution x, = and x, = can bo read lrom the resulting system. Thus, the system nas a un que solulion. To show thai the given system of equations has an infinite number of soluions Tot =2, gin by subsitutirig i=2 into sach equation, and then collect ali vanables terms on tie left sde. 3x1- 4x;
Use the Gauss-Jordan elimination algorithm to show that the following system of equations has a unique solution forr=3, but an infinite number of solutions for r= 2. 3x,- 4X2 = X1 X1-2x2 = rX2 The solution x, = and x, F can be read from the resulting system. Thus, the system has a unique solution. X1 To show that the given system of equations has an infinite number of solutions for r= 2, begin by substituting r=2 into each equation, and then collect all variables terms on the left side 3x, - 4x2 2x, X1 - 2x, = 2x, (Simplify your answers.) Next, eliminate x, from the second equation. Adding times the first equation to the second equation changes the second equation to (Simplify your answers.) Interpret the resulting system of equation. Choose the correct answer below and complete the corresponding answer box(es) to complete your choice. (Simplify your answers.) O A. The first equation implies that X, and the second equation implies that X2 = Since these answers are not equal, no free variables exist. Therefore, the system has an infinite number of solutions. O B. The first equation implies that x1 but there is no equation for x, Evidently, x2 is a free variable and any value can be assigned to it. Therefore, the system has an infinite number of solutions. O C. The first equation implies that x1 and the second equation implies that x, Since these answers are equal, a free variable exists. Therefore, the system has an infinite number of solutions.
Transcribed Image Text:Use the Gauss-Jordan elimination algorithm to show that the following system of equations has a unique solution forr=3, but an infinite number of solutions for r= 2. 3x,- 4X2 = X1 X1-2x2 = rX2 The solution x, = and x, F can be read from the resulting system. Thus, the system has a unique solution. X1 To show that the given system of equations has an infinite number of solutions for r= 2, begin by substituting r=2 into each equation, and then collect all variables terms on the left side 3x, - 4x2 2x, X1 - 2x, = 2x, (Simplify your answers.) Next, eliminate x, from the second equation. Adding times the first equation to the second equation changes the second equation to (Simplify your answers.) Interpret the resulting system of equation. Choose the correct answer below and complete the corresponding answer box(es) to complete your choice. (Simplify your answers.) O A. The first equation implies that X, and the second equation implies that X2 = Since these answers are not equal, no free variables exist. Therefore, the system has an infinite number of solutions. O B. The first equation implies that x1 but there is no equation for x, Evidently, x2 is a free variable and any value can be assigned to it. Therefore, the system has an infinite number of solutions. O C. The first equation implies that x1 and the second equation implies that x, Since these answers are equal, a free variable exists. Therefore, the system has an infinite number of solutions.
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