Solve the system of linear equations below using Gaussian Elimination X1 + x2 + x3 + X4 = 10 -X2 + 2x, + 3xX3 – 4x4 = -7 = 54 11x4 – 2x3 + 4x2 + 8x1 Хз — 4x2 + 9х, — х2 %3D —6 %3D

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CT: Test
Problem 15CT
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1. Solve the system of linear equations below using Gaussian Elimination
X1 + x2 + x3 + X4 = 10
—х2 + 2х, + 3х; — 4x, 3 —7
= 54
11x4 — 2хз + 4х2 + 8х1
Хз — 4x2 + 9х, — х2 %3D —6
2. Decompose your coefficient matrix in question 1 into a lower and upper triangular
matrices
3. Use LU matrices found in question 2 to find the inverse of the coefficient matrix
Transcribed Image Text:1. Solve the system of linear equations below using Gaussian Elimination X1 + x2 + x3 + X4 = 10 —х2 + 2х, + 3х; — 4x, 3 —7 = 54 11x4 — 2хз + 4х2 + 8х1 Хз — 4x2 + 9х, — х2 %3D —6 2. Decompose your coefficient matrix in question 1 into a lower and upper triangular matrices 3. Use LU matrices found in question 2 to find the inverse of the coefficient matrix
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