(A) Answer The form of matrix equation is [ − 2 − 3 6 1 ] [ x 1 x 2 ] = [ − 4 − 36 ] Explanation Given: The system of linear equation − 2 x 1 − 3 x 2 = − 4 6 x 1 + x 2 = − 36 Concept used: The Matrix equation A X = B Where A is the coefficient matrix of the system X And B are column matrices The column matrix B is also called a constant matrix its entries are the constant terms in the system of equation Calculation: The system of linear equation − 2 x 1 − 3 x 2 = − 4 6 x 1 + x 2 = − 36 The Matrix equation A X = B ................. ( 1 ) Where A is the coefficient matrix of the system X And B are column matrices A = [ − 2 − 3 6 1 ] , X = [ x 1 x 2 ] , B = [ − 4 − 36 ] From equation (1) [ − 2 − 3 6 1 ] [ x 1 x 2 ] = [ − 4 − 36 ] (B) To determine To find: The matrix by using the Gauss-Jordan elimination on augmented matrix [ A : B ] Answer The Gauss-Jordan elimination on augmented matrix A = [ − 7 6 ] Explanation Given: The system of linear equation − 2 x 1 − 3 x 2 = − 4 6 x 1 + x 2 = − 36 Concept used: The Gauss-Jordan elimination on augmented matrix [ A : B ] :-An elementary row operations are applied to a matrix to obtain a (row-equivalent) row echelon form of the matrix. A second method of elimination is called Gauss-Jordan elimination Calculation: The system of linear equation − 2 x 1 − 3 x 2 = − 4 6 x 1 + x 2 = − 36 The Matrix equation A X = B ................. ( 1 ) Where A is the coefficient matrix of the system X And B are column matrices A = [ − 2 − 3 6 1 ] , X = [ x 1 x 2 ] , B = [ − 4 − 36 ] The augmented matrix A = [ − 2 − 3 : − 4 6 1 : − 36 ] R 2 → R 2 + 3 R 1 A = [ − 2 3 : − 4 0 − 8 : − 48 ] A = [ − 7 6 ]

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 8.2, Problem 59E

(A)

To determine

To find:

The given system of linear equations in the form of matrix equation

(A)

Expert Solution

Answer to Problem 59E

The form of matrix equation is $[−2−361][x1x2]=[−4−36]$

Explanation of Solution

Given:

The system of linear equation

$−2x1−3x2=−46x1+x2=−36$

Concept used:

The Matrix equation

$AX=B$

Where A is the coefficient matrix of the system

$X$ And $B$ are column matrices

The column matrix $B$ is also called a constant matrix its entries are the constant terms in the system of equation

Calculation:

The system of linear equation

$−2x1−3x2=−46x1+x2=−36$

The Matrix equation

$AX=B.................(1)$

Where A is the coefficient matrix of the system

$X$ And $B$ are column matrices

$A=[−2−361], X=[x1x2], B=[−4−36]$

From equation (1)

$[−2−361][x1x2]=[−4−36]$

(B)

To determine

To find:

The matrix by using the Gauss-Jordan elimination on augmented matrix $[A:B]$

(B)

Expert Solution

Answer to Problem 59E

The Gauss-Jordan elimination on augmented matrix $A=[−76]$

Explanation of Solution

Given:

The system of linear equation

$−2x1−3x2=−46x1+x2=−36$

Concept used:

The Gauss-Jordan elimination on augmented matrix $[A:B]$ :-An elementary row operations are applied to a matrix to obtain a (row-equivalent) row echelon form of the matrix. A second method of elimination is called Gauss-Jordan elimination

Calculation:

The system of linear equation

$−2x1−3x2=−46x1+x2=−36$

The Matrix equation

$AX=B.................(1)$

Where A is the coefficient matrix of the system

$X$ And $B$ are column matrices

$A=[−2−361], X=[x1x2], B=[−4−36]$

The augmented matrix

$A=[−2 −3:−4 6 1 :−36]R2→R2+3R1A=[−2 3: −4 0 −8: −48]A=[−76]$

Chapter 8.2, Problem 58E

Chapter 8.2, Problem 60E

Chapter 8 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The given system of linear equations in the form of matrix equation

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To find: The given system of linear equations in the form of matrix equation

Answer to Problem 59E

Explanation of Solution

To find: The matrix by using the Gauss-Jordan elimination on augmented matrix [A:B]<m:math><m:mrow><m:mrow><m:mo>[</m:mo><m:mrow><m:mi>A</m:mi><m:mo>:</m:mo><m:mi>B</m:mi></m:mrow><m:mo>]</m:mo></m:mrow></m:mrow></m:math>

Answer to Problem 59E

Explanation of Solution

Chapter 8 Solutions

To find:

The given system of linear equations in the form of matrix equation

To find:

The matrix by using the Gauss-Jordan elimination on augmented matrix $[A:B]$