Question

Use Gauss-Jordan method (augmented matrix method) to solve the following systems of linear equations. Indicate whether the system has a unique solution, infinitely many solutions, or no solution. Clearly write the row operations you use. (a) (5 points) x + y + z = 6 2x − y − z = 3 x + 2y + 2z = 0 (b) (5 points) x − 2y + z = 4 3x − 5y + 3z = 13 3y − 3z = −9

Answer #1

Use Gauss-Jordan method (augmented matrix method) to
solve the following systems of linear equations.
Indicate whether the system has a unique solution, infinitely many
solutions, or no solution. Clearly write
the row operations you use.
(a)
x − 2y + z = 8
2x − 3y + 2z = 23
− 5y + 5z = 25
(b)
x + y + z = 6
2x − y − z = 3
x + 2y + 2z = 0

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

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...

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

Write the system of equations as an augmented matrix. Then solve
the system by putting the matrix in reduced row echelon form.
x+2y−z=-10
2x−3y+2z=2
x+y+3z=0

Use Gauss-Jordan Elimination to solve the following system of
equations. Please show all the wotk identifying what row operations
you are doing in each step
2x-4y+6z-8w=-10
x-2y+z+w=2
-2x+4y+z+2w=-3
-x+3y-3z+5w=6

1. Solve by via Gauss-Jordan elimination:
a) 2y + 3z = 8
2x + 3y + z =
5
x − y − 2z =
−5
b) x + 3y + 2z = 5
x −
y + 3z = 3
3x + y + 8z = 10
c) 3x1 + x2 + x3 + 6x4 = 14
x1 − 2x2 +
5x3 − 5x4 = −7
4x1 + x2 + 2x3 + 7x4 =
17

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...

1. (RREF) Solve the systems by Gauss-Jordan method. State the
rank of the matrix of coeffi-cients.
(a) x+y+z=46x−y+z=94x+y+2z=10
(b) x+y+2z=02x−y+z=14x+y+5z=1

Use an inverse matrix to solve (if possible) the system of
linear equations. (If there is no solution, enter NO SOLUTION.)
4x
−
2y
+
3z
=
−16
2x
+
2y
+
5z
=
−30
8x
−
5y
−
2z
=
30

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