To determine To solve : The system of linear equations by Gauss-Jordan elimination method. 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 sub matrix 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, 3 x 1 + x 2 − 2 x 3 = 2 x 1 − 2 x 2 + x 3 = 3 2 x 1 − x 2 − 3 x 3 = 3 Solve the given system of linear equations by Gauss-Jordan elimination method as follows. The augmented matrix is, [ 3 1 − 2 2 1 − 2 1 3 2 − 1 − 3 3 ] . Perform the below operations to reduce the matrix. [ 3 1 − 2 2 1 − 2 1 3 2 − 1 − 3 3 ] ∼ [ 1 2 1 − 1 1 − 2 1 3 2 − 1 − 3 3 ] R 1 − R 3 → R 1 ∼ [ 1 2 1 − 1 0 − 4 0 4 2 − 1 − 3 3 ] R 2 − R 1 → R 2 ∼ [ 1 2 1 − 1 0 1 0 − 1 2 − 1 − 3 3 ] R 2 ( − 4 ) → R 2 Further perform the row operation R 3 + R 2 → R 3 as follows

16th Edition

ISBN: 9781323174869

Author: Barnett

Publisher: PEARSON EDUCATION (COLLEGE)

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 4.3, Problem 2MP

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 1MP

Chapter 4.3, Problem 3MP

Students have asked these similar questions

The maximum capacity spanning tree problem is as follows for a given graph G = (V, E) withcapacities c(uv) on the edges. The capacity of a tree T is defined as the minimum capacity of anedge in T. The maximum capacity spanning tree problem is to determine the maximum capacity ofa spanning tree.(i) Describe how to modify the input graph to find a maximum weight spanning tree making use ofa minimum weight spanning tree algorithm.(ii) Show that a maximum (weight) spanning tree is also a maximum capacity spanning tree.(iii) Is the converse of part (ii) true? That is, is it true that a maximum capacity spanning tree is alsoa maximum spanning tree? Either give counterexamples (of all sizes) or a proof.(iv) Prove the following max-min result. The maximum capacity of a spanning tree is equal to theminimum bottleneck value of a cut. For a subset U ⊆ V , the cut [U, V − U] is the set of edgesbetween U and V − U. The bottleneck value of a cut [U, V − U] is the largest capacity among theedges of…

1) Find The inverse The domain of m(x) = tion and of the function The inverse function 3- √x-a

Prove that the following version of a greedy algorithm produces a minimum spanning tree in aweighted graph. Start with a vertex v as the initial tree and at each stage add an edge with minimumweight having exactly one end in the current tree. Stop when all vertices have been added

Chapter 4 Solutions

COLLEGE MATH FOR MATH2040 RMU PKG

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.