Consider the following system of linear equations. 2x+12y=-16 4x+26y=-42 Solve the system by completing the steps below to produce a reduced row-echelon form. R, and R, denote the first a notation ( means the expression/matrix on the left becomes the expression/matrix on the right once the row opera

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 4CEXP
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Jordan elimination with a 2x2 matrix
Consider the following system of linear equations.
2x+12y=-16
4x+26y= -42
Solve the system by completing the steps below to produce a reduced row-echelon form. R, and R, denote the first a
notation () means the expression/matrix on the left becomes the expression/matrix on the right once the row opera
(a) For each step below, enter the coefficient for the row operation. The
first matrix in Step 1 is the augmented matrix for the given system of
equations.
Step 1:
0-R, - R,
|1 6 1
2 12
-16
4 26
-42
4 26 1
-42
Step 2:
R
1 6
-8
-8
0 2
-10
4 26
-42
Check
Explanation
02020 McGraw-HI Education
Transcribed Image Text:Jordan elimination with a 2x2 matrix Consider the following system of linear equations. 2x+12y=-16 4x+26y= -42 Solve the system by completing the steps below to produce a reduced row-echelon form. R, and R, denote the first a notation () means the expression/matrix on the left becomes the expression/matrix on the right once the row opera (a) For each step below, enter the coefficient for the row operation. The first matrix in Step 1 is the augmented matrix for the given system of equations. Step 1: 0-R, - R, |1 6 1 2 12 -16 4 26 -42 4 26 1 -42 Step 2: R 1 6 -8 -8 0 2 -10 4 26 -42 Check Explanation 02020 McGraw-HI Education
Step
IR, + R, - R,
1.
-8
2
1 6
-8
4 26 1
-42
0 2
| -10
Step 3:
|1 6
D-R, - R.
1 6 -8
-8
0 2
-10
0 1
-5
Step 4: Enter the coefficient for the row operations and the missing entries
in the resulting matrix.
0R, - R, - R,
1 0
1 6
-8
1
-5
(b) Give the solution.
Transcribed Image Text:Step IR, + R, - R, 1. -8 2 1 6 -8 4 26 1 -42 0 2 | -10 Step 3: |1 6 D-R, - R. 1 6 -8 -8 0 2 -10 0 1 -5 Step 4: Enter the coefficient for the row operations and the missing entries in the resulting matrix. 0R, - R, - R, 1 0 1 6 -8 1 -5 (b) Give the solution.
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