Question

1. a) Find the solution to the system of linear equations using matrix row operations. Show all your work.

x + y + z = 13

x - z = -2

-2x + y = 3

b) How many solutions does the following system have? How do you know?

6x + 4y + 2z = 32

3x - 3y - z = 19

3x + 2y + z = 32

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) (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 =...

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

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

Solve the system of linear equations. If the system has an
infinite number of solutions, set w = t and solve for x, y, and z
in terms of t.)
x + y + z + w = 6
2x+3y - w=6
-3x +4y +z + 2w= -1
x + 2y - z + w = 0
x, y, z, w=?

Consider the system of linear equations 2x+y-3z=-7 x+y-z=-1
4x+3y-5z=-9 (a)Represent this system as a matrix A (b)Use row
operations to transform A into row echelon form Use your answer to
(b) to find all non-integer solutions of the system

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)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 system of equations using matrices. Make a 4x4 matrix and
get the diagonal to be ones and the rest of the numbers to be
zeros
2x -3y + z + w = - 4
-x + y + 2z + w = 3
y -3z + 2w = - 5
2x + 2y -z -w = - 4

his is a linear algebra problem
Determine the values of a for which the system has no
solutions, exactly one solution, or infinitely many solutions.
x + 2y - 2z = 3
3x - y + 2z = 3
5x + 3y + (a^2 - 11)z = a + 6
For a = there is no solution.
For a = there are infinitely many solutions.
For a ≠ ± the system has exactly one solution.

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