8.Solve the linear system Ax-b byx₁ + x₂-3x₂ = -1-x₁ + 2x₂ = 1x₁ - x₂ + x₂ = 2a) finding the LU-factorization of the coefficient matrix Ab) Solving the lower triangular system Ly-b.c)solving the upper triangular system Ux-y.

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Answered: 8. Solve the linear system Ax-b by x₁ +…

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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2x+y=z=7 -3x + 2y + z = -1 x + 3z = 0 and remembering our equation AX = B, answer the following questions. a) Write down what A, X, and B are. b) Does A-¹ exist? If so, what is A-¹? c) Solve the system of equations using the coefficient matrix. In other words, find X. (1)
Write the system of linear equations in the form Ax = b. Then use Gaussian elimination to solve this matrix equation for x. X2 + x3 = -6 - 3x1 - 2x1 + 4x2 5x3 = 5 X1 2x2 + 3x3 = 0 X1 8- X2 = X3 X1 349 X2 5 X3 0 сл
Consider the system of linear equations: -x1 + 2x2 + 3x3 + x4 = 3 2x1 - 4x2 + x3 + 2x4 = -1 -3x1 + 8x2 + 4x3 - x4 = 6 x1 + 4x2 + 7x3 - 2x4 = -4 i) Solve the systems of equations for x1, x2, x3, x4 utitilizing the Gauss-Jordan method. ii) Obtain the Lower & Upper triangular matrices for the system of linear equations. iii) Use the LU factorization obtained in iii) to solve for x1, x2, x3, x4. N.b : Don't kindly lift answers from other experts solution.
Consider the following linear equations: -2x + 4y + 10z = -5 -2x + (22-k)y+9z = -3 -2x + 4y+(12-k)z =k+9 a) Suppose the above equation is expressed as Ax = b with x = equations in one matrix form as (Alb)= -2 -2 -2 4 -2 10 4 X3 10 -5 b) Use row operations on (Alb) by substracting row 1 from row 2 and row 3 respectively. Fill in the missing entries: Express the coefficients of the -5 Submit part 3 marks Unanswered
) Let 3 -3 -5 -8 -1 B = 3 -4 -3 2 (a) Find the reduced row echelon form of the matrix B. rref(B) : (b) How many pivot columns does B have?
Write the system of linear equations in the form Ax = b. Then use Gaussian elimination to solve this matrix equation for x. X2 + x3 = -6 - 3x1 - 2x1 + 4x2 5x3 = 5 X1 2x2 + 3x3 = 0 X1 8- X2 = X3 X1 349 X2 5 X3 0 сл
The vector (8, 0, 1) is a solution of the linear system: X1 + 4x2 – 4x3 = 4 5x] + 16х2 — 16х3 — 24 -x1 – 2x2 + 2x3 = -6 O True O False
I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3
Consider the system: x+2y+3z=6 2x + 5y +3z=7 x + 8z = 14 a. Write the system as a matrix equation in the form of Ax = b b. Find A-¹ using elementary row operations and the inverse algorithm (show steps completely and carefully. No technology). c. Solve the system Ax = b using your result from part (b) and matrix multiplication. Show the basic steps (though you do not need to show the detail of the matrix multiplication process -- that can be done "in your head"). Your solution should be written as x = (a column matrix, as required for the multiplication)
(c) Consider the system 2х1 — бх, — Хз — 38 — Зх1 — х2 + 7Хз :-34 -8x1 + x2 – 2x3 = -20 (i) Write the system in AX = B. 1 0 | and 23/10 1. (ii) Given the decomposition of matrix A is L= -3/2 -4 -6 -1 -43 b -11 -5 a 1 U = (0 -10 and the Al: 11/2 -373/20, -62 373 -11 C -20/ Find a, b and c.

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8. Solve the linear system Ax-b by x₁ + x₂-3x₂ = -1 -x₁ + 2x₂ = 1 x₁ - x₂ + x₂ = 2 a) finding the LU-factorization of the coefficient matrix A b) Solving the lower triangular system Ly-b. c) solving the upper triangular system Ux-y.