1. Determine whether each of the given points below is a solution of the linear systemx1 + 6x2 + 2x3 – 5x4 − 2x52x38x4- X5-43X5 = 7.==(a) (0,0,5,0,7)(b) (1,1,1,1,1)How many solutions exist for this system? Justify your response.(c) (-6,1,5,0,7)

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Answered: 1. Determine whether each 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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Need only a handwritten solution only (not a typed one).
2.) Use the rank criterium to find out whether the following System of linear equations has a solution : x₁ + x₂ + x3 - 2xy =0 2X₂+3x₂ = 1 3X₁ X₂ + x3 + xy = 3 4x1 +2х3 тохи = 5
Consider the three systems of linear equations: 4x₁ + 6x2 + 2x3 + 8x4 6x₁ + 9x2 + 16x4 2x1 + 3x2 - 2x3 + 7x4 Select one: O a. none of the others b. (A) O c. (A) and (B) are equivalent (A) and (C) are equivalent d. (B) and (C) are equivalent e. (A), (B) and (C) are equivalent = 2 4 2 = = 4x₁ + 6x2 + 2x3 + 8x4 (B) 2x₁ + 3x2 + 4x3 + x4 2x1 + 3x2 - 2x3 + 7x4 2 = 0 2 = || || = (C) 2x1 + 3x2 + x3 + 4x4 3x3 - 3x4 -3x3 + 3x4 = = = 1 -1 1
How can x-5= x + 6 be set up as a system of equations? O 2y + x = -10 3y + x = 18 O2y + 2x = -10 3y + 3x = 18 O2y-x= -10 3y - x = 18 O2y-2x = -10 3y - 3x = 18
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The eigenvalues of the coefficient matrix A are given. Find a general solution of the indicated system x′=Ax. x′= 75 16 −32 −72 −13 32 144 32 −61 x; λ=−5, 3, 3 x(t)=enter your response here

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1. Determine whether each of the given points below is a solution of the linear system x1 + 6x2 + 2x3 - 5x4 - 2x5 2x38x4 - = −4 X5 = 3 X5 = 7. (a) (0,0,5,0,7) (b) (1,1,1,1,1) How many solutions exist for this system? Justify your response. (c) (-6,1,5,0,7)