3- solve the following system of linear equations using Gaussian elimination approach (backward substitution). 1x₁ + x₂ + 2x₂ = 3 [1 1 2 2x₁ + 3x₂ + x3 =1} Ax=b, A = 2 3 3x₁x₂x3 = -1) 3 -1 -1 Write the corresponding LU decomposition. Write the determinant of coefficient matrix based on LU results. b= 3
3- solve the following system of linear equations using Gaussian elimination approach (backward substitution). 1x₁ + x₂ + 2x₂ = 3 [1 1 2 2x₁ + 3x₂ + x3 =1} Ax=b, A = 2 3 3x₁x₂x3 = -1) 3 -1 -1 Write the corresponding LU decomposition. Write the determinant of coefficient matrix based on LU results. b= 3
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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Question
![3- solve the following system of linear equations using Gaussian elimination approach (backward
substitution).
1x₁ + x₂ + 2x₂ = 3
1
1 2
2x₁ + 3x₂ + x3 =1} Ax=b, A = 2 3
3x₁x₂x3 = -1
3
-1 -1
Write the corresponding LU decomposition.
Write the determinant of coefficient matrix based on LU results.
Give the inverse of A using the L¹, U-¹
b=
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7448293a-a6c3-49b9-b972-361b3f7e11c8%2F9b4fcf12-ed91-4623-9779-641ac8a67ab9%2F5sl6z58_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3- solve the following system of linear equations using Gaussian elimination approach (backward
substitution).
1x₁ + x₂ + 2x₂ = 3
1
1 2
2x₁ + 3x₂ + x3 =1} Ax=b, A = 2 3
3x₁x₂x3 = -1
3
-1 -1
Write the corresponding LU decomposition.
Write the determinant of coefficient matrix based on LU results.
Give the inverse of A using the L¹, U-¹
b=
3
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