Consider the following system of linear equations. 4x+12y=-24 -8x-20y=36 Solve the system by completing the steps below to produce a reduced row-echelon form. R₁ and R, denote the first and second rows, respectively. The arrow notation (→) means the expression/matrix on the left becomes the expression/matrix on the right once the row operations are performed. (a) For each ste

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Systems Of Equations And Inequalities
Section6.2: Two-variable Linear Systems
Problem 5ECP
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Consider the following system of linear equations.
4x+12y=-24
-8x-20y=36
Solve the system by completing the steps below to produce a reduced row-echelon form. R, and R₂ denote the first and second rows, respectively. The arrow
notation (→) means the expression/matrix on the left becomes the expression/matrix on the right once the row operations are performed.
(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:
4
-8 -20
12 1 -24
36
Step 2:
- 20
36
R₁ R₁
R₁ + R₂-
→ R₂
-8
3
- 20
36
CD
8 08
X
3
Transcribed Image Text:Consider the following system of linear equations. 4x+12y=-24 -8x-20y=36 Solve the system by completing the steps below to produce a reduced row-echelon form. R, and R₂ denote the first and second rows, respectively. The arrow notation (→) means the expression/matrix on the left becomes the expression/matrix on the right once the row operations are performed. (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: 4 -8 -20 12 1 -24 36 Step 2: - 20 36 R₁ R₁ R₁ + R₂- → R₂ -8 3 - 20 36 CD 8 08 X 3
Step 2:
1
3 1 -6
-8 -20 36
Step 3:
[63]
04
-6
- 12
1
-6
[3]
X =
(b) Give the solution.
R₁ + R₂ R₂
R₂ R₂
-
y = 0
R₂ + R, R₁
3
4
[3]
Step 4: Enter the coefficient for the row operations and the missing entries
in the resulting matrix.
6
12
-6
-3
0
(316
Transcribed Image Text:Step 2: 1 3 1 -6 -8 -20 36 Step 3: [63] 04 -6 - 12 1 -6 [3] X = (b) Give the solution. R₁ + R₂ R₂ R₂ R₂ - y = 0 R₂ + R, R₁ 3 4 [3] Step 4: Enter the coefficient for the row operations and the missing entries in the resulting matrix. 6 12 -6 -3 0 (316
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