Consider the following problem:Maximize z = 1 - 2x2 + 3x3 - 3x₁subject tox1 + 2x2 - x3+4x4≤2-1 + 2x2 + 3x3 + 2x4≤11, 2, 3, 4 ≥0Give the matrix associated with the problem in standard form. How many possiblebases does the problem have? Give a feasible basis that is not given only by slackvariables and the basic feasible solution that corresponds to it. Is this solutiondegenerate or non-degenerate? Show that the given solution is a basic solution.feasible. Provide B, у в.

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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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Gaussian elimination with partial pivoting is applied to the matrix [2 1 0 3; -5 1 2 0; -2 0 1 2; -4 -4 -5 1] a) m41= -2 b) m41= -2/5 c) m41= 4/5 d) m41= 5/2
2. A is a 4 x 5 matrix with four pivot positions. a) Does the equation Ax = 0 have a nontrivial solution? b) Does the equation Ax = b have at least one solution for every possible b?
8. (i)Redo: For what type of square matrices A will the algebraic system Ax = 2x have solutions other than x = 0? { Here x is an nx1 real matrix & A is an nxn real matrix.} Hints: 1) Ix = x. 2) Use GP appropriately; 3) Such matrices A must satisfy a certain relation.
- About linear algebra, matrices, etc. Suppose the matrix (A mxn) has n pivot columns. Explain why, for every b E R^N, the equation Ax = b has at most one solution.(Hint: Explain why Ax = b cannot have an multitude/infinity of solutions.) - The question also follows in the image below.
You are given the 3 × 3 linear system in augmented matrix form 5 0 -1 2 0 1 0 2 0 0 2 4 Starting from an initial guess of xo = [1, 1, 1]", what is the result of the first iteration of the Gauss-Seidel method?
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2. Is the following matrix in reduced row echelon form? If not, how would we reduce it to reduced row echelon form? Choose the correct option below. 00 1 0 1 1 0 -2 0. 4 0 (a) The matrix is already in RREF. (b) The matrix is not yet in RREF, and one row scaling will reduce it to RREF. (c) The matrix is not yet in RREF, and one row swap will reduce it to RREF. (d) The matrix is not yet in RREF, and one row replacement will reduce it to RREF. (e) The matrix is not yet in RREF, and at least two row operations are required to reduce it to RREF. O (a) is the correct answer O (b) is the correct answer O (c) is the correct answer (d) is the correct answer O (e) is the correct answer
Put the following program in matrix standard form Minimize Z= 2X₁-2X2+4X3 Subjected to: 5X₁+2X₂-3X32-7 2X₁-2X₂+4X3 <8 With X₁: Non negetive
If the columns of a 7x7 matrix D are linearly independent, what can you say about solutions of Dx=b? why?
Solve the given linear programming problem using the Duality Method. Show work by creating the primal and dual augmented matrices, setting up the initial simplex tableau, circling the first pivot element, and giving the final simplex tableau. State the optimal solution and the optimal value for the final answer. Minimize: C= 24x+18y+24z Subject to: 3x+2y+z>=4 x+y+3z>=6 x>=0, y>=0, z>=0
Determine the set of all basic solutions and basic feasible solutions of the following poly- hedron: P = {x € R4 : 3x1 – 4x2 + 2x3 – x4 = 1; –2x1 + 2x2 – x3 + x4 = 1; x > 0}. For each basic solution and basic feasible solution, determine whether it is degenerate or nondegenerate. You can assume that the coefficient matrix A has full row rank.
4. The final simplex matrix for a problem is shown below. Give the solutions to both the maximization problem and the dual minimization problem based on this final matrix. Carefully label each solution. x2 x3 S1 S2 S3 P 1 -0.5 3 -0.7 29 1 -0.8 -2 -0.5 47 -0.6 -1 -2.4 1 53 15 7 13 1 597 O O o-

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