Explanation Approach: A system of linear equations can be written in the form of A X = B where A is called the coefficient matrix, B is called the known matrix, and X is called the variable matrix. If a square matrix A of dimension 2 × 2 has an inverse A − 1 , and if X is a variable matrix and B is a known matrix both with n rows, then the solution of the matrix equation A X = B is given as follows. X = A − 1 B . Take a 3 × 6 matrix with left half as matrix B and right half as I 3 and transform the left half into identity matrix by performing elementary row operations on the entire matrix, the right half becomes inverse of the matrix B . Calculation: The given system of linear equations { 2 x + 4 y + z = 7 − x + y − z = 0 x + 4 y = − 2 can be written as a single matrix equation A X = B as follows: [ 2 4 1 − 1 1 − 1 1 4 0 ] [ x y z ] = [ 7 0 − 2 ] Here, A = [ 2 4 1 − 1 1 − 1 1 4 0 ] , B = [ 7 0 − 2 ] , and X = [ x y z ] . Now the solution of this matrix equation is given by X = A − 1 B . First, find A − 1 , Now we take a matrix of dimension 3 × 6 with left half as matrix A and right half as I 3 and perform row operations to transform the left half into I 3 . [ 2 4 1 1 0 0 − 1 1 − 1 0 1 0 1 4 0 0 0 1 ] R 1 ↔ R 3 → [ 1 4 0 0 0 1 − 1 1 − 1 0 1 0 2 4 1 1 0 0 ] R 2 → R 2 + R 1 → [ 1 4 0 0 0 1 0 5 − 1 0 1 1 2 4 1 1 0 0 ] R 3 → R 3 − 2 R 1 → [ 1 4 0 0 0 1 0 5 − 1 0 1 1 0 − 4 1 1 0 − 2 ] R 2 → 1 5 R 2 → [ 1 4 0 0 0 1 0 1 − 1 5 0 1 5 1 5 0 − 4 1 1 0 − 2 ] R 3 → R 3 + 4 R 2 → [ 1 4 0 0 0 1 0

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 11.3, Problem 43E

To determine

To solve:

The system of equations {2x+4y+z=7−x+y−z=0x+4y=−2 by converting it into a matrix equation and find the values of x, y and z.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 42E

Chapter 11.3, Problem 44E

Students have asked these similar questions

2. A microwave manufacturing firm has determined that their profit function is P(x)=-0.0014x+0.3x²+6x-355 , where is the number of microwaves sold annually. a. Graph the profit function using a calculator. b. Determine a reasonable viewing window for the function. c. Approximate all of the zeros of the function using the CALC menu of your calculator. d. What must be the range of microwaves sold in order for the firm to profit?

A clothing manufacturer's profitability can be modeled by p (x)=-x4 + 40x² - 144, where .x is the number of items sold in thousands and p (x) is the company's profit in thousands of dollars. a. Sketch the function on your calculator and describe the end behavior. b. Determine the zeros of the function. c. Between what two values should the company sell in order to be profitable? d. Explain why only two of the zeros are considered in part c.

CCSS REASONING The number of subscribers using pagers in the United States can be modeled by f(x) = 0.015x4 -0.44x³ +3.46x² - 2.7x+9.68 where x is the number of years after 1990 and f(x) is the number of subscribers in millions. a. Graph the function. b. Describe the end behavior of the graph. c. What does the end behavior suggest about the number of pager subscribers? d. Will this trend continue indefinitely? Explain your reasoning.

Chapter 11 Solutions

Algebra and Trigonometry

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

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

The system of equations { 2 x + 4 y + z = 7 − x + y − z = 0 x + 4 y = − 2 by converting it into a matrix equation and find the values of x , y and z .

Solution Summary: The author explains how the system of linear equations c2x+4y+z=7 can be written as a single matrix equation AX=B.

Videos

To solve:

The system of equations {2x+4y+z=7−x+y−z=0x+4y=−2 by converting it into a matrix equation and find the values of x, y and z.

Want to see the full answer?

Chapter 11 Solutions

The system of equations { 2 x + 4 y + z = 7 − x + y − z = 0 x + 4 y = − 2 by converting it into a matrix equation and find the values of x , y and z .

Solution Summary: The author explains how the system of linear equations c2x+4y+z=7 can be written as a single matrix equation AX=B.

Videos

To solve: The system of equations {2x+4y+z=7−x+y−z=0x+4y=−2 by converting it into a matrix equation and find the values of x, y and z.

Want to see the full answer?

Chapter 11 Solutions

To solve:

The system of equations {2x+4y+z=7−x+y−z=0x+4y=−2 by converting it into a matrix equation and find the values of x, y and z.