Number 6 1-14 GAUSS ELIMINATIONSolve the linear system given explicitly or by its augmentedmatrix. Show details.1. 4x6y=-113.5.7.9.11.- 3x + 8y98y + 6z = -6-2x + 4y - 6z = 401312 -6-47 -7315711x + y =2=2-14410- 13410 6-2y2z = -83x + 4y - 5z = 130 5 5 -10-3 -311Z =10-20062. [3.04.6.8.10.02-2 41.545-94-135-0.54.51-15-32x3x + 2y-8010.62 -56.02 -1 5316-21-6 14y + 3z = 8z = 2= 54-7 321 -927175012.13.14.-312 -2 43 -6-3w2w +8w3-1210x + 4y17x +x +y34x + 16y3 153-7y +050- 1110z =15-251 - 1342 -715. Equivalence relation. By definition, an equivalencerelation on a set is a relation satisfying three conditions:(named as indicated)(i) Each element A of the set is equivalent to itself(Reflexivity).(ii) If A is equivalent to B, then B is equivalent to A(Symmetry).015–4-32z =2z ==0-4264(iii) If A is equivalent to B and B is equivalent to C,then A is equivalent to C (Transitivity).Show that row equivalence of matrices satisfies thesethree conditions. Hint. Show that for each of the threeelementary row operations these conditions hold.

6.The given augmented matrix of the linear system,The aim is to find the solution to the system of…

Answered: 16 -21 6. 4 -8 3 -1 2 -5 3 -6 1 7

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16 -21 6. 4 -8 3 -1 2 -5 3 -6 1 7

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

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ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

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Chapter6: Exponential Functions And Sequences

Section: Chapter Questions

Problem 3CA

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Question

Number 6

1-14 GAUSS ELIMINATION
Solve the linear system given explicitly or by its augmented
matrix. Show details.
1. 4x6y=-11
3.
5.
7.
9.
11.
- 3x + 8y
9
8y + 6z = -6
-2x + 4y - 6z = 40
13
12 -6
-4
7 -73
157
11
x + y =
2
=
2
-1
4
4
10
- 13
4
1
0 6
-2y2z = -8
3x + 4y - 5z = 13
0 5 5 -10
-3 -3
1
1
Z =
1
0
-2
0
0
6
2. [3.0
4.
6.
8.
10.
0
2
-2 4
1.5
4
5
-9
4
-1
3
5
-0.5
4.5
1
-15
-3
2x
3x + 2y
-8
0
1
0.6
2 -5
6.0
2 -1 5
3
16
-21
-6 1
4y + 3z = 8
z = 2
= 5
4
-7 3
21 -9
2
7
17
50
12.
13.
14.
-3
1
2 -2 4
3 -6
-3w
2
w +
8w
3
-1
2
10x + 4y
17x +
x +
y
34x + 16y
3 1
5
3
-7
y +
0
5
0
- 11
10z =
1
5
-2
5
1 - 1
3
4
2 -7
15. Equivalence relation. By definition, an equivalence
relation on a set is a relation satisfying three conditions:
(named as indicated)
(i) Each element A of the set is equivalent to itself
(Reflexivity).
(ii) If A is equivalent to B, then B is equivalent to A
(Symmetry).
0
15
–4
-3
2z =
2z =
=
0
-4
2
6
4
(iii) If A is equivalent to B and B is equivalent to C,
then A is equivalent to C (Transitivity).
Show that row equivalence of matrices satisfies these
three conditions. Hint. Show that for each of the three
elementary row operations these conditions hold.

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(a) How do Gaussian elimination and Gauss-Jordan elimination differ? (b) Use Gauss-Jordan elimination to solve the linear system in part 3(d).
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