Question

Determine if the given system is consistent. Do not completely solve the system.

2x_1 + 4x_3 = 8

x_2 - 2x_4 = 2

-5x_2 + 4x_3 + 2x_4 = 2

4x_1 + 6x_4 = -2

Choose the correct answer below.

A.

The system is consistent because the augmented matrix of the system
cannot be reduced to triangular form.

B.

The system is consistent because the augmented matrix of the system
can be reduced to triangular form.

C.

The system is inconsistent because the augmented matrix of the
system cannot be reduced to triangular form.

D.

The system is inconsistent because the augmented matrix of the
system can be reduced to triangular form.

Answer #1

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

In problems 1-10 do the following • Solve the given system by
systematic elimination of unknowns using an augmented matrix. •
Check you answers. • Give a geometric interpretation of your
solution in terms of the graphs of the equations in the system.
3u - 2v = -1
-5u + 3v = 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 augmented matrix below represents a system of linear
equations associated with a real world prob-
lem. The augmented matrix has already been completely row
reduced.
1 0 6 12 0 1 −2 0 0000
(a) Use the reduced matrix to write down the parametric solution
for the system as a point (x, y, z).
(b) Assuming that x, y, and z represent the number of whole
items, determine how many “actual” solutions this system has, and...

Solve the system
-2x1+4x2+5x3=-22
-4x1+4x2-3x3=-28
4x1-4x2+3x3=30
a)the initial matrix is:
b)First, perform the Row Operation 1/-2R1->R1. The resulting
matrix is:
c)Next perform operations
+4R1+R2->R2
-4R1+R3->R3
The resulting matrix is:
d) Finish simplyfying the augmented mantrix down to reduced row
echelon form. The reduced matrix is:
e) How many solutions does the system have?
f) What are the solutions to the system?
x1 =
x2 =
x3 =

Complete the following steps: Create a system of linear
equations that is consistent.
graph your system of linear equations.
Determine the number of solutions of your system.
Create a system of linear equations that is inconsistent.
graph your inconsistent system of linear equations.
Create a system of linear equations that is dependent.
graph your dependent system of linear equations
. Part II: Based on your work in Part I, discuss the following:
Discuss how you can verify that the system...

Solve the following system of linear equations: 3x2−9x3 = −3
x1−2x2+x3 = 2 x2−3x3 = 0 If the system has no solution, demonstrate
this by giving a row-echelon form of the augmented matrix for the
system. If the system has infinitely many solutions, your answer
may use expressions involving the parameters r, s, and t. You can
resize a matrix (when appropriate) by clicking and dragging the
bottom-right corner of the matrix.

Solve the system of equations using matrices. Use the Gaussian
elimination method with back-substitution.
{3a - b -3c = 13
{2a - b + 5c = -5
{a + 2b - 5c = 10
Use the Gaussian elimination method to obtain the matrix in
row-echelon form. Choose the correct answer below.
The solution set is {(_,_,_,_)}

Given a matrix system AX = B as below, where A is a 4 x 4
matrix as given below
A:
2
1
0 0
1
2
1 0
0
2
4 1
0
0
1 3
B:
0
-1
3
-1
Solve for all 4 X values using TDMA
algorithm
First identify the a, d, c and b values for each row, and then
find P’s and Q’s and finally determine X’s.

Use Gaussian elimination to find the complete solution to the
following system of equations, or show that none exists.
{-x + y + z = -1
{-x + 5y -15z = -29
{ 7x - 6y - 11z = 0
Find the row-echelon form of the matrix for the given system of
equations.
(Do not include the vertical bar in the augmented matrix.)
Select the correct choice below and, if necessary, fill in the
answer boxes to complete your choice....

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