Express the solutions of the given homogeneous system as a linear combination of basicsolutions.- 20x20x- 4xSolutions:100y ++ 100y(x, y, z) = S20y +100z =100z =20z+t=000where s, t E RFill in the two basic solutions as vectors, using < and > as enclosing brackets.

The given homogeneous system,We have to find the solution of this system.

Answered: Express the solutions of the given…

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
1. form: Solve the system of equations. Put your solutions, if there is one, in parametric X1 + -X1 + 2x1 X2 + 3x2 - X3 = 0 + 2x3 = 0 X3 = 0 ||
Is Vector Y in the Column space of A? What is the solution set? Write y as an appropriate linear combination. 8 1 9 a = (-5 9 -1 Y= %3D 10 8
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Write the solution set of the homogeneous system in parametric vector form. X1 + 3x2+ X3 =0 =0 -2x13x24x3 -3x2 + 2x3 = 0
Let a₁ = 12 - [ 4 ] → - [ ¹2 ], and b - [44] = = a₂ -12 48 Is b a linear combination of a₁ and a₂? OA. b is not a linear combination. B. Yes b is a linear combination. C. We cannot tell if b is a linear combination. Either fill in the coefficients of the vector equation, or enter "NONE" if no solution is possible. a₁ + b = 8₂
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. 3x₁ + 3x₂ +6x3 = 12 - 9x1 - 9x2 - 18x3 = - - 36 - 6x2 - 18x3 = 18 Describe the solution set, x = O of the first system of equations in parametric vector form. Select the correct X2 X3 choice below and fill in the answer box(es) within your choice. (Type an integer or fraction for each matrix element.) O A. X= B. X=X₂ C, X= D. X=X₂ + X3 3x₁ + 3x₂ + 6x3 = 0 - 9x1 - 9x2 - 18x3 = 0 - 6x2 - 18x3 = 0 + X3
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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. 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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Express the solutions of the given homogeneous system as a linear combination of basic solutions. - 20x 20x - 4x Solutions: 100y + + 100y 20y (x, y, z) = S + 100z = 100z = 20z = +t 0 0 0 where s, t E R Fill in the two basic solutions as vectors, using < and > as enclosing brackets.