Number 6Describe the solutions of the following system in parametricvector form. Also, give a geometric description of the solutionset.= 1X1 + 3X,-4x, – 9X,+ X2.3.9х. + 2х1= -16X3-3х, — 6х, — -1.

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Answered: Number 6 Describe the solutions of the…

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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Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 2x₁ + 2x2 + 4x3 = 8 2x₁ + 2x₂ + 4x3 = 0 - 6x₁ - 6x2 - 12x3 = 0 - 6x₁ - 6x2 - 12x3 = -24 - 4x2 - 12x3 = 12 - 4x2 - 12x3 = 0 Describe the solution set, x = X3 (Type an integer or fraction for each matrix element.) O A. X= B. X=X₂ OC. X= O D. X=X₂ +X3 X1 X2 of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within your choice. +X3
(part 1 of 4) Suppose you start at the origin in 3-space, move along the x-axis a distance of 2 units in the positive direction, and then move down- ward a distance of 3 units. What are the coordinates of your position? 1. (2,0, -3) 2. (2, -3,0) 3. (2,0,3) 4. (0, 2, -3) 5. (0, -3,2) (part 2 of 4) Which one of the points P(6, 9, -3), Q(8, -2, -8), R(-5, 8, 1) in 3-space is closest to the xz-plane? 1. R(-5, 8, 1) 2. P(6, 9, -3) 3. Q(8, -2, -8) (part 3 of 4) A rectangular box is constructed in 3-space with one corner at the origin and other ver- tices at (1,0,0), (0,3,0), (0,0,2). Find the length of the diagonal of the box. 1. length 14 2. length 3. length 4. length 5. length 6. length = = = = √22 √14 √19 19 22 (part 4 of 4) What are the coordinates of the projection of the point Q(-4, 5, 3) onto the zx-plane? 1. (-4, 0, 3) 2. (-4, -5, 3) (4, 5, 3) 3. 4. (-4, 5, 0) 5. (-4, 5, -3) 6. (0,5, 3)
Find an equation the plane that passes through the points A(4,0, –5), B(8,-3,-6), and C (1, 2, -1). Write your final answer in standard form.
Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 4x₁ +4x2 + 8x3 = 16 - 12x₁-12x₂-24x3 = - 48 - 6x₂ + 12x3 = 12 X₁ Describe the solution set, x= x₂ 4 X3 4x₁ + 4x2 + 8x3 = 0 - 12x₁-12x₂ - 24x3 = 0 - 6x₂ + 12x3 = 0 of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or fraction for each matrix element.)

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Number 6 Describe the solutions of the following system in parametric vector form. Also, give a geometric description of the solution set. X. + 3) *1+ 3X, + x, = 1 — 4х, — 9х, + 2х, 3 — 1 3. -4x. 1 2X,= -1 - -3x, – 6x, = -1. 2.