Question

Aumented Matrix using elimination method for solving a system of linear equations. Apply row operations to the augmented matrix until reduced to an identity matrix.

4x + 2y + 7z = 35

3x + y + 8z = 25

5x + 37 + z = 40

Answer #1

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

Sec 6.2
1.Write an augmented matrix for the following system of
equations.
9x-8y+6z=-1
7x-5y+2z=9
6y-8z=-9
The entries in the matrix are ?
2.use row operations on the augmented matrix as far as necessary
to to determine whether they system is independent, dependent, or
inconsistent ?
4x-6y+5x=-2
-8x+12y-10z=4
-12x+18y-15z=6
3. use row operations on the augmented matrix as far as
necessary to to determine whether they system is independent,
dependent, or inconsistent ?
5x-7y+4z=13
-5x+7y-4z=-15
-10x+14y-8z=-27
4. Solve the system by...

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 =...

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

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

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

Apply the row operation R1 + 2R3 → R1 on the following
matrix:
2 −3 1 4
2 0 6 −5
1 −1 1 0
−→
(h) True or False: The point (2, 1) is in the following feasible
region:
x + 2y ≤ 5, 5x − 6y < 7, and x ≥ 0, y ≥ 0.
(i) True or False: (x = −1, y = 2, z = 3) is a solution to the
following...

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 following system of equations using Matrix Algebra
with Excel
7X + 4Y - 8Z
= 50
5X
- 3Y + 5Z = 45
3X
+ 2Y + 2Z = 40

1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

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