2. Use LU decomposition with partial pivoting to solve the following problem.2x₁ +5x₂ + x₂ = -72x₂ + 4x₂ = 66x₁ + x₂ = 12Include in your results the results of the decomposition for L and U, the d vector found in the forwardsubstitution step and the final values for the x vector.Remember, any row shifts must include the right-hand column.

The given equations are: 2x1+5x2+x3=-72x2+4x3=66x1+x2=12 We have to solve the given equation using…

Answered: 2. Use LU decomposition with partial…

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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Solve the given set of equations by applying L-U decomposition method. The upper triangular matrix U should include 1’s on its diagonal. -2.2a-5.72b-2.64c=-11.44 2.5a+4.1b+9.72c=1.576 -a-0.5b-5.68c=3.116
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2. Use LU decomposition with partial pivoting to solve the following problem. 2x₁ +5x₂ + x3 = -7 2x₂ + 4x₂ = 6 6x₁ + x₂ = 12 Include in your results the results of the decomposition for L and U, the d vector found in the forward substitution step and the final values for the x vector.