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: 8220100548512

Author: Watson

Publisher: CENGAGE L

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

Solve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8

5. Solve for the matrix X. (Hint: we can solve AX -1 = B whenever A is invertible) 2 3 0 Χ 2 = 3 1

Write p(x) = 6+11x+6x² as a linear combination of ƒ (x) = 2+x+4x² and g(x) = 1−x+3x² and h(x)=3+2x+5x²

Chapter 11 Solutions

EBK 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.