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Solution of Systems of Linear Algebraic Equations Quiz 4: Our Biggest Dreams Deserve Our Greatest Efforts

This document is a quiz for a linear algebra class that contains 3 problems testing different methods for solving systems of linear equations. Problem 1 has two parts testing the inverse matrix method and Gauss-Jordan method. Problem 2 has two parts testing Cramer's rule and Gaussian elimination. Problem 3 has three parts testing LU decomposition, Gauss-Seidel method, and Jacobi method. The quiz is signed by the instructor Engr. Herbert V. Villaruel and wishes the student good luck.

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52 views1 page

Solution of Systems of Linear Algebraic Equations Quiz 4: Our Biggest Dreams Deserve Our Greatest Efforts

This document is a quiz for a linear algebra class that contains 3 problems testing different methods for solving systems of linear equations. Problem 1 has two parts testing the inverse matrix method and Gauss-Jordan method. Problem 2 has two parts testing Cramer's rule and Gaussian elimination. Problem 3 has three parts testing LU decomposition, Gauss-Seidel method, and Jacobi method. The quiz is signed by the instructor Engr. Herbert V. Villaruel and wishes the student good luck.

Uploaded by

kurou hazama
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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NATIONAL UNIVERSITY

COLLEGE OF ENGINEERING
SOLUTION OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS
QUIZ 4
Instruction: Solve the following. Show your detailed solution.
1.) Find the solution of the given systems of linear equations based on the given method:
−𝟗𝐰 − 𝟏𝟖𝐱 − 𝟗𝐲 − 𝟏𝟔𝐳 = 𝟏𝟑𝟒
𝟓𝐰 − 𝐱 − 𝟏𝟓𝐲 + 𝟕𝐳 = −𝟑𝟗
−𝟒𝐰 − 𝟗𝐱 + 𝟏𝟏𝐲 − 𝟏𝟒𝐳 = 𝟏𝟑𝟎
𝟏𝟕𝐰 − 𝟑𝐱 − 𝟏𝟐𝐲 + 𝟖𝐳 = 𝟐𝟐

a) Inverse Matrix Method (15 pts.)


b) Gauss-Jordan Method (15 pts.)
2.) Find the solution of the given systems of linear equations based on the given method:
−𝟏𝟗𝐀 + 𝟓𝐂 − 𝟗𝐃 = 𝟏𝟑𝟗
𝐀 − 𝟑𝐁 − 𝟔𝐂 + 𝟔𝐃 = 𝟏𝟔
−𝟒𝐀 − 𝟖𝐁 + 𝟖𝐂 − 𝟏𝟔𝐃 = 𝟓𝟔
−𝟏𝟎𝐀 − 𝟏𝟔𝐁 + 𝐂 − 𝟐𝐃 = 𝟏𝟕𝟑

a) Cramer’s Rule (10 pts.)


b) Gaussian Elimination Method (15 pts.)
3.) Find the solution of the given systems of linear equations based on the given method:
𝟑𝑨 + 𝟕𝑩 + 𝟏𝟑𝑪 = 𝟕𝟔
𝑨 + 𝟓𝑩 + 𝟑𝑪 = 𝟐𝟖
𝟏𝟐𝑨 + 𝟑𝑩 − 𝟓𝑪 = 𝟏

a) LU Decomposition Method (15 pts.)


b) Gauss-Seidel Method [Show the complete table. Use: %e ≤ 0.005] (15 pts.)
c) Jacobi Method [Show the complete table. Use: %e ≤ 0.005] (15 pts.)
ENGR. HERBERT V. VILLARUEL OUR BIGGEST DREAMS DESERVE OUR GREATEST EFFORTS.
INSTRUCTOR God bless on your quiz, future engineer!

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