Explanation Given Information: The provided system of equations is: − 2 x + 5 y − 4 z = − 20 x − 2 y + z = 8 x − 5 y + 9 z = 24 Formula used: Let A be an n × n matrix for which A − 1 exists and let I n be the n × n identity matrix. To find A − 1 , Step1: Write a matrix of the form [ A | I n ] . Step2: Perform row operations to write the matrix in the form [ I n | B ] . Step3: The matrix B is A − 1 . If A X = B represents a system of n linear equations in n variables with a unique solution. Then, X = A − 1 B Where, A is the coefficient matrix, X is the column matrix of variables and B is the column matrix of constants. Calculation: Consider the provided system of equations: − 2 x + 5 y − 4 z = − 20 x − 2 y + z = 8 x − 5 y + 9 z = 24 Convert this system of equation into matrix equation of the form A X = B as: [ − 2 5 − 4 1 − 2 1 1 − 5 9 ] [ x y z ] = [ − 20 8 24 ] Now, consider the inverse for the matrix, A = [ − 2 5 − 4 1 − 2 1 1 − 5 9 ] Now, write the matrix in the form [ A | I 3 ] as: [ A | I 3 ] : [ − 2 5 − 4 1 0 0 1 − 2 1 0 1 0 1 − 5 9 0 0 1 ] Now, perform the row operations to transform left side of the matrix to the 3 × 3 identity matrix or to get [ I 3 | B ] as: Apply the operation R 1 ⇔ R 2 in above matrix and simplify as, [ − 2 5 − 4 1 0 0 1 − 2 1 0 1 0 1 − 5 9 0 0 1 ] → R 1 ⇔ R 2 [ 1 − 2 1 0 1 0 − 2 5 − 4 1 0 0 1 − 5 9 0 0 1 ] Apply the operation 2 R 1 + R 2 → R 2 and − R 1 + R 3 → R 3 in above matrix and simplify further as, [ 1 − 2 1 0 1 0 − 2 5 − 4 1 0 0 1 − 5 9 0 0 1 ] → 2 R 1 + R 2 → R 2 − R 1 + R 3 → R 3 [ 1 − 2 1 0 1 0 0 1 − 2 1 2 0 0 − 3 8 0 − 1 1 ] Apply the operation 2 R 2 + R 1 → R 1 and 3 R 2 + R 3 → R 3 in above matrix and simplify further as, [ 1 − 2 1 0 1 0

2nd Edition

ISBN: 9781259986017

Author: Miller

Publisher: MCG CUSTOM

See similar textbooks

Videos

Question

Chapter 6.4, Problem 46PE

To determine

To calculate: The solution of the provided system of equations,

−2x+5y−4z=−20x−2y+z=8x−5y+9z=24

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 45PE

Chapter 6.4, Problem 47PE

Chapter 6 Solutions

COLLEGE ALGEBRA-W/ACCESS >CUSTOM<

Ch. 6.1 - Skill Practice 1. a. Write the augmented...Ch. 6.1 - Skill Practice Use the matrix from Example 2 to...Ch. 6.1 - Skill Practice 3. Solve the system by using...Ch. 6.1 - Skill Practice Solve the system by using...Ch. 6.1 - Prob. 5SP Ch. 6.1 - 1. A rectangle array of elements is called a...Ch. 6.1 - Prob. 2PE Ch. 6.1 - Explain the meaning of the notation R2R3.Ch. 6.1 - Explain the meaning of the notation R2R3.Ch. 6.1 - Explain the meaning of the notation 3R1R1.

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 solution of the provided system of equations, − 2 x + 5 y − 4 z = − 20 x − 2 y + z = 8 x − 5 y + 9 z = 24

Solution Summary: The author explains how to convert the provided system of equations into a matrix equation of the form AX=B.

Videos

To calculate: The solution of the provided system of equations,

−2x+5y−4z=−20x−2y+z=8x−5y+9z=24

Want to see the full answer?

Chapter 6 Solutions

The solution of the provided system of equations, − 2 x + 5 y − 4 z = − 20 x − 2 y + z = 8 x − 5 y + 9 z = 24

Solution Summary: The author explains how to convert the provided system of equations into a matrix equation of the form AX=B.

Videos

To calculate: The solution of the provided system of equations, −2x+5y−4z=−20x−2y+z=8x−5y+9z=24

Want to see the full answer?

Chapter 6 Solutions

To calculate: The solution of the provided system of equations,

−2x+5y−4z=−20x−2y+z=8x−5y+9z=24