For numbers 27, 29, and 31, how am I supposed to do these? It must be with the left-to-right elimination method, which is shown on the 2nd picture. Please include step by step instructions and solutions different planes may intersect in a single point (as when two walls meet the ceiling), may inter-sect in a line (as in a paddle wheel), or may not have a common intersection. (See Figures 1.28,1.29, and 1.30.) Thus three linear equations in three variables may have a unique solution,infinitely many solutions, or no solution. For example, the solution of the system3x + 2y + z = 6x - y - z = 0x + y - z = 4is x = 1, y = 2, z = -1 because these three values satisfy all three equations and theseare the only values that satisfy them. In this section, we will discuss only systems of threelinear equations in three variables that have unique solutions. Additional systems will bediscussed in Section 3.3, "Gauss-Jordan Elimination: Solving Systems of Equations."We can solve three equations in three variables using a systematic procedure called theleft-to-right elimination method.CeilingWallWallLoileInfinitely manysolutionsUnique solutionNo solutionFigure 1.28Figure 1.29Figure 1.30LEFT-TO-RIGHT ELIMINATION METHODted dProcedureExampleTo solve a system of three equations in three variables bythe left-to-right elimination method:2x + 4y + 5z = 4Solve:x - 2y - 3z = 5x + 3y + 4z = 11. If necessary, interchange two equations or use multi-plication to make the coefficient of the first variablein equation (1) a factor of the other first variablecoefficients.1. Interchange the first two equations.x - 2y - 3z = 52x + 4y + 5z = 4x + 3y + 4z = 12. Add (-2) × equation (1) to equation (2) and add(-1) X equation (1) to equation (3).x - 2y - 3z =Ox + 8y + 11z = -6Ox + 5y + 7z = -4(1)(2)(3)2. Add multiples of the first equation to each of thefollowing equations so that the coefficients of thefirst variable in the second and third equationsbecome zero.(1)(2)(3)3. Add a multiple of the second equation to the thirdequation so that the coefficient of the second variablein the third equation becomes zero.3. Add (-) × equation (2) to equation (3).x - 2y - 3z =8y + 11z = -6(1)(2)Oy + -z =8(3)4. Solve the third equation and back substitute from thebottom to find the remaining variables.4. z = -2from equation (3)y = -(-6 - 11z) = 2from equation (2)x = 5 + 2y + 3z = 3so x = 3, y = 2, z = -2from equation (1) 3x052y = 8 –y = 9-23.24.3x2xy = 5 +3v =- 145x + 3y = -225.S4x – 5y = -3|2x - 7y = -626.(3x + 7y 4Use the left-to-right elimination method to solve the sys-tems in Problems 27-32.x + 2y + z =- 2y + 2z = -10mony + 4z = – 1027.28.ord bo + 3z = 8adi aiy o blo 2z = 10-3z =6.s ofx-yー 8z=0.x + 3y - 8z = 2029.y + 4z =8.30.y - 3z = 113y + 14z = 222y + 7z = -4x + 4y – 2z =x – 3y – z = 0x – 2y + z = 82x- 6y + z = 631.x + 5y + 2z = -2 32.x + 4y - 28z = 22APPLICATIONS33. Temperatures and traveling When U.S. citizens travelabroad, they need some understanding of Celsiustemperature readings-does one need mittens if thetemperature will be 20°C? A quick conversion formulaoften used by tour guides to give a rough Fahrenheitequivalent for a Celsius reading is

“Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: x + 2y + z = 2 .000S -y + 3z = 8 orl…

x + 2y + z = 2 .000S -y + 3z = 8 orl brito viauosil 2z = 10 %3D %3D

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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