Problem 1.4. Solve the following linear system for the variables x,y,z,wand write the solution in vector form5x4x+ y +2 ++Zx + 9y + 2zW = 53w= 02w = 5

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Answered: Problem 1.4. Solve the following linear…

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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6. Consider the following system of four linear equations in five variables. 2x1 + 4x2 – 2x3 + 2x4 + 4x3 = 2 xị+ 2x2 – x3+ 2x4 = 4 3x1 + 6x2 – 2x3 + x4 + 9x5 = 1 5x1 + 10r2 – 4x3 + 5x4 + 9x5 = 9 | (a) Write a vector equation that is equivalent to this linear system, and a matrix equation that is equivalent to this linear system. (b) Determine the solution set of this linear system, and express it in parametric vector form.
Consider the following system of two linear equations: +y = 0 2x + 3y = 15 select the graph that correctly displays this system of equations and point of ntersection. а.) 3. (3,3) 2 -7 -6 -5 -4 -3 -2 -1 1 4 5 6 -1 -2 -3 -4 -5 -6 -7 4 3 1 -7 -6 -5 -4 -3 -2 -1 1 2. 3 4 -1 -2 (3,-3) -3 -4 -5 -6 -7
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Consider the following linear equations: 2т - у- 62 — 5у - 2 4.x + y - z 3. -2, = -8, 13. Use Gauss elimination method with partial pivoting to solve the above
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i) Solve the following system of equations using Gauss (or Gauss-Jordan) elimination: 3x+y =-2 4x +3y=-1 -2x+y =3 ii) Based ONLY on your answer in part (i) and without doing any extra work, answer True or False to the following statements and briefly explain why they are True or False (no explanation: no marks). 1) Vector w = (-2, -1, 3) belongs to the spanning set of vectors u = (3, 4, -2) and v = (1, 3, 1). 2) The set S = {(-2, -1, 3), (3, 4, -2), (1, 3, 1)} is a basis for its spanning set. 3) The following system of equations has a unique solution: 3x +y -2z=-1 4x +3y-z =0 -2x+y +3z=4
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2. a) Given the following system of linear equations: -6+ 10 *+y+=5 2x-y+=9 x-2y+3z =16 Detemine the values of x, y and z using the Cramer's rule.
4. . Solve the linear equation systems 2x, +5x₂ + 2x, = -8 by using Crout method, where (x₁+2x₂ + 3x₂ = -3 fed arti hai (25) 3x₁ + x₂ + 5x₂ = 1 [1 2 3 -4 U = 0 1 001

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Problem 1.4. Solve the following linear system for the variables x,y,z, w nd write the solution in vector form +9y+ 5x 4x 2 + W = 5 Z + + 3w 2w x + 9y + 2z - = 0 5