Consider the system of equations shown below.- 4y 16-2. ty 2(a) Determine whether the nonhomogeneous system Ax bis consistent.O consistentO inconsistent(b) af the system ia consistent, then write the solution in thex,X where x, isa particular solution of Axband x, is a solution of Ax-0. the nystem is inconsistent, enter INCONSISTENT in both matrices.)

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Answered: Consider the system of equations shewn…

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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Is it possible that all solutions of a homogeneous system of twelve linear equations in fourteen variables are multiples of one fixed nonzero solution? Discuss. Consider the system as Ax = 0, where A is a 12x 14 matrix. Choose the correct answer below. O A. Yes. Since A has at most 12 pivot positions, rank As 12. By the Rank Theorem, dim Nul A = 14- rank Az 2. Since there is at least one free variable in the system, all solutions are multiples of one fixed nonzero solution. O B. No. Since A has 12 pivot positions, rank A= 12. By the Rank Theorem, dim Nul A = 12 - rank A= 0. Since Nul A = 0, it is impossible to find a single vector in Nul A that spans Nul A. OC. No. Since A has at most 12 pivot positions, rank As 12. By the Rank Theorem, Nul A= 14 - rank Az 2. Thus, it is impossible to find a single vector in Nul A that spans Nul A. O D. Yes. Since A has 12 pivot positions, rank A= 12. By the Rank Theorem, dim Nul A= 12- rank A= 0. Thus, all solutions are multiples of one fixed nonzero…
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a11 a12 a13 1 Let A = a21 a22 a23 be the matrix whose inverse is A-1 = -1 Find the value of x3 in the unique solution to the system of linear a31 a32 a33 4 equations: a11x1 + a12X2 + a13X3 a21x1 + a22 X2 + a23X3 2 a31x1 a32X2 a33 X3 3 А. 10 В. 3 С. —2 D. 0 Е. 17 || ||
M Inbox (x | My My Driv x → > C You Tub x = Footba x W Week 2 x webassign.net/web/Student/Assignment-Responses/submit?dep-31310967&tags-autosave#Q20 Use an inverse matrix to solve each system of linear equations. (a) x₁ + 2x₂ + x3 = -2 X1 X1 + 2x2x3 = -4 x₁2x2 + x3 = 2 ([ (X1, X2, X3) = (b) x₁ + 2x2 + x3 = 1 X₁ + 2x₂ - X3 = 1 X1 - 2x2 + x3 = -3 (X₁, X2, X3) = Need Help? Submit Answer Read It 1) MindTa x XE Ryan C XE Basket x Submit Assignment Save Assignment Prog
The given matrix represents an augmented matrix for a linear system. 1 4 -6 -3 -12 18 8 -12 | Write the corresponding set of linear equations for the system. How many unknowns are in the system? Number of unknown(s): 2 ▼ Use Gaussian elimination to solve the linear system. Introduce free parameters as necessary, using r, s, t if needed. X1 X2 =
5
3x 2 1-2 0 0 3 --(3) -- 67 9) --C) --(2) (129) A == B 0 D = 5 -3 -1 -4 -2 3 Where possible, find the following. If not possible give the reason. (a) AB (b) DA (c) B+C (d) 2D + BC (e) AC (f) What is the value of x for which A does not have an inverse.

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