Explanation Procedure used: Gauss-Jordan Elimination: Step 1: Choose the leftmost nonzero column and use appropriate row operations to get a 1 at the top. Step 2: Use multiples of the row containing the 1 from step 1 to get zeroes in all remaining places in the column containing this 1. Step 3: Repeat step 1 with the submatrix formed by (mentally) deleting the row used in step 2 and all rows above this row. Step 4: Repeat step 2 with the entire matrix, including the rows deleted mentally. Continue this process until the entire matrix is in reduced form. Calculation: The given system of linear equations is, x 1 − 2 x 2 + x 3 + x 4 + 2 x 5 = 2 − 2 x 1 + 4 x 2 + 2 x 3 + 2 x 4 − 2 x 5 = 0 3 x 1 − 6 x 2 + x 3 + x 4 + 5 x 5 = 4 − x 1 + 2 x 2 + 3 x 3 + x 4 + x 5 = 3 Solve the given system of linear equations by Gauss-Jordan elimination method as follows. The augmented matrix for the given system of equations is, [ 1 − 2 1 1 2 2 − 2 4 2 2 − 2 0 3 − 6 1 1 5 4 − 1 2 3 1 1 3 ] Perform the row operations to reduce the matrix as shown below. Since, the pivot element is found in the first row, perform the row operations to eliminate the first row. [ 1 − 2 1 1 2 2 − 2 4 2 2 − 2 0 3 − 6 1 1 5 4 − 1 2 3 1 1 3 ] ∼ [ 1 − 2 1 1 2 2 0 0 4 4 2 4 0 0 − 2 − 2 − 1 − 2 0 0 4 2 3 5 ] R 2 + 2 R 1 → R 2 R 3 − 3 R 1 → R 3 R 4 + R 1 → R 4 ∼ [ 1 − 2 1 1 2 2 0 0 1 1 0.5 1 0 0 − 2 − 2 − 1 − 2 0 0 4 2 3 5 ] 1 4 R 3 → R 3 ∼ [ 1 − 2 0 0 1.5 1 0 0 1 1 0.5 1 0 0 0 0 0 0 0 0 0 − 2 1 1 ] R 1 − R 2 → R 1 R 3 + 2 R 2 → R 3 R 4 − 4 R 2 → R 4 ∼ [ 1 − 2 0 0 1.5 1 0 0 1 1 0

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134674148

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4.3, Problem 69E

To determine

To solve: The system of linear equations by Gauss-Jordan elimination method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.3, Problem 68E

Chapter 4.3, Problem 70E

Students have asked these similar questions

Suppose that 80% of athletes at a certain college graduate. You randomly select eight athletes. What’s the chance that at most 7 of them graduate?

Suppose that you flip a fair coin four times. What’s the chance of getting at least one head?

Suppose that the chance that an elementary student eats hot lunch is 30 percent. What’s the chance that, among 20 randomly selected students, between 6 and 8 students eat hot lunch (inclusive)?

Chapter 4 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 4.1 - Solve by graphing and check: 2x − y = −3 x + 2y =...Ch. 4.1 - Solve each of the following systems by graphing: x...Ch. 4.1 - Prob. 3MP Ch. 4.1 - Prob. 4MP Ch. 4.1 - Prob. 5MP Ch. 4.1 - Prob. 6MP Ch. 4.1 - Prob. 7MP Ch. 4.1 - Prob. 1ED Ch. 4.1 - Prob. 2ED Ch. 4.1 - In Problems 1–6, find the x and y coordinates of...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.