Question

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 system of linear equations:

x + 2y − z = 0; 3x + 3y + z = 6; 5x + 3y − z = 6

Pag

Answer #2

answered by: anonymous

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

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

2.Use separation of variables to solve (3x^2(1-y^2))/2y with
initial condition y(1)=2.
3.State the solution of the homogeneous ODE with roots of its
characteristic equation of r= 1,1,1,+-7i,3+-5i.
4.Consider the system of linear equations:
2x+6y+z=7
x+2y-z=-1
5x+7y-4z=9
solve this system using: a) Carmer's rule, b)Gauss-Jordan
elimination, c) an inverse matrix.

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...

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

Write the augmented matrix of the given system of equations.
x + y - z = 8
5x - 3y = 4
6x + 2y - z = 2

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

Solve the following system using augmented matrux methods
-3x+6y = 0
-4x +6y = 0
a) The initial matrix is:
b) First, perform the Row Operation 1/-3R1->R1. The resulting
matrix is:
c) Next, perform the operation +3R1+R2->R2. The resulting
matrix is:
d) Finish simplifying the augmented matrix. The reduced matrix
is:
e) How many solutions does the system have?
f) What are the solutions to the system?
x =
y =

The following constraints of a linear programming model have
been graphed on the graph paper provided (same constraints found in
problem #3) to form a feasible region:
2X + 6Y
>= 120
10X + 2Y > = 200
X +
Y <= 120
X
<= 100
Y <= 80
X,Y
>= 0
Using the graphical method, determine the optional solution and
the objective function value for the following objective functions.
Graph the objective function as a dashed line on...

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