Consider the following system of linear equations. 4x-2y -z = 14 +2z = 26 =-3 5x 2x +y Solve the system by completing the steps below to produce a reduced row-echelon form. R₁, R₂, and R3 denote the first, second, and third rows, respectively. The arrow notation (→) stands for "replaces," where the expression on the left of the arrow replaces the expression on the right.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 29HP
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Consider the following system of linear equations.
4x-2y z 14
5x
+2z = 26
2x +y
=-3
Solve the system by completing the steps below to produce a reduced row-echelon form.
R₁, R₂, and R3 denote the first, second, and third rows, respectively.
The arrow notation (→) stands for "replaces," where the expression on the left of the arrow replaces the expression on the
right.
Here is the augmented matrix:
Enter the missing coefficients for the row operations.
(1)
(2)
(3)
(4)
R₁ R₁:
(-5) R₁ + R₂ R₂:
R₁ + R3 R3:
R₂ → R₂:
( 2 ) +
•R₂ + R₁ R₁:
4 - 2 -1
5
0
2
2 1
R₂ + R3 → R₂:
1
5
2
1
O
1
10
-|C
01
1
2
0
1
-|C
2
1
2
0 2
1
0
2 4
13
13
10
2
1
4
-|-
-IN
-|4
13
21
10
14
26
-3
71
26
N
17
- 10
7
2
17
5
- 10
25 55 55
26
17
84
010
8
X
Transcribed Image Text:Consider the following system of linear equations. 4x-2y z 14 5x +2z = 26 2x +y =-3 Solve the system by completing the steps below to produce a reduced row-echelon form. R₁, R₂, and R3 denote the first, second, and third rows, respectively. The arrow notation (→) stands for "replaces," where the expression on the left of the arrow replaces the expression on the right. Here is the augmented matrix: Enter the missing coefficients for the row operations. (1) (2) (3) (4) R₁ R₁: (-5) R₁ + R₂ R₂: R₁ + R3 R3: R₂ → R₂: ( 2 ) + •R₂ + R₁ R₁: 4 - 2 -1 5 0 2 2 1 R₂ + R3 → R₂: 1 5 2 1 O 1 10 -|C 01 1 2 0 1 -|C 2 1 2 0 2 1 0 2 4 13 13 10 2 1 4 -|- -IN -|4 13 21 10 14 26 -3 71 26 N 17 - 10 7 2 17 5 - 10 25 55 55 26 17 84 010 8 X
(2)
(3)
(4)
(5)
(6)
(-5) R₁ + R₂ R₂:
Solution:
R₁ + R₂ R3:
(1)-R₂
(-¾ )
R₂ → R₂:
x =
R₂ + R₁ R₁:
R₂ + R3 R3:
R₂ R3:
•R3 + R₁ → R₁ :
R₂ + R₂ → R₂:
0
y = 0
0
1
01
N/U
01
10
0 2
00
1 0
0 1
1
2
00
1
2
z =
1 0 0
-0
S|N
2539
010
10
13
001
10
1
1
4
13
4
21
10
1
4
13
10
1
Enter the missing coefficient for the row operation, fill in the missing matrix
entries, and give the solution.
N
26
5
17
5
8
2
17
2
- 10
7
2
17
5
- 10
5
17
5
84
5
Transcribed Image Text:(2) (3) (4) (5) (6) (-5) R₁ + R₂ R₂: Solution: R₁ + R₂ R3: (1)-R₂ (-¾ ) R₂ → R₂: x = R₂ + R₁ R₁: R₂ + R3 R3: R₂ R3: •R3 + R₁ → R₁ : R₂ + R₂ → R₂: 0 y = 0 0 1 01 N/U 01 10 0 2 00 1 0 0 1 1 2 00 1 2 z = 1 0 0 -0 S|N 2539 010 10 13 001 10 1 1 4 13 4 21 10 1 4 13 10 1 Enter the missing coefficient for the row operation, fill in the missing matrix entries, and give the solution. N 26 5 17 5 8 2 17 2 - 10 7 2 17 5 - 10 5 17 5 84 5
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