Question

What is the difference between the *Gauss
Elimination Method* **and** *Gauss Elimination
Method with partial pivoting* **and**
*Gauss-Jordan Elimination Method* while finding a solution
for a linear system?

*I mean the difference in the steps of the
solution*

Answer #1

Use Gauss
Elimination with partial pivoting method to find x1, x2,and x3 for
the following set of linear equations. You should show all your
work in details. Verify your solutions
2X1
+ X2 - X3 = 1
5X1
+ 2X2 + 2X3 = -4
3X1
+ X2 + X3 = 5

1)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express your answer in terms
of the parameters t and/or s.)
x1
+
2x2
+
8x3
=
6
x1
+
x2
+
4x3
=
3
(x1,
x2, x3)
=
2)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express...

Solve the system of linear equations using the Gauss-Jordan
elimination method
x − 5y = 24
4x + 2y = 8 (x, y) =

Solve the system of linear equations using the Gauss-Jordan
elimination method.
2x
+
2y
+
z
=
7
x
+
z
=
2
4y
−
3z
=
21

2. Solve the system of linear equations by using the
Gauss-Jordan (Matrix) Elimination Method. No credit in use any
other method. Use exactly the notation we used in class and in the
text. Indicate whether the system has a unique solution, no
solution, or infinitely many solutions.In the latter case,present
the solutions in parametric form
x+2y+3z=7
-12z=24
-10y-5z=-40

4. Solve the system of linear equations by using the
Gauss-Jordan (Matrix) Elimination Method. No credit in use any
other method. Use exactly the notation we used in class and in the
text. Indicate whether the system has a unique solution, no
solution, or infinitely many solutions. In the latter case, present
the solutions in parametric form.
3x + 6y + 3z = -6
-2x -3y -z = 1
x +2y + z = -2

PLEASE WORK THESE OUT!!
A) Solve the system of linear equations using the Gauss-Jordan
elimination method.
2x
+
10y
=
−1
−6x
+
8y
=
22
x,y=_________
B) If n(B) = 14, n(A ∪
B) = 30, and n(A ∩ B) = 6, find
n(A).
_________
C) Solve the following system of equations by graphing. (If
there is no solution, enter NO SOLUTION. If there are infinitely
many solutions, enter INFINITELY MANY.)
3x
+
4y
=
24
6x
+
8y...

in the Gauss Elimination, what is the
difference between the forward substitution and the backward
substitution?

Solve the system using either Gaussian elimination with
back-substitution or Gauss-Jordan elimination. (If there is no
solution, enter NO SOLUTION. If the system has an infinite number
of solutions, express x1,
x2, and x3 in terms of the
parameter t.)
2x1
+
3x3
=
3
4x1
−
3x2
+
7x3
=
4
8x1
−
9x2
+
15x3
=
13
(x1,
x2, x3) =
()

Use Gauss-Jordan elimination to solve the following systems of
linear equations, or state that there are no solutions.
a)
4?+8?=−4
−3?−6?=5
b)
?+4?−?=8
2?+8?+?=1
you should find that the system has infinitely many solutions.
Introduce a parameter in order to give the general solution. Then
give one particular solution.

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