Question

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.

A. There is one solution. The solution set is {(_, _, _)}

(Simplify your answers.)

B. There are infinitely many solutions. The solution set is {(_, _, z)}where z is any real number.

(Type expressions using z as the variable. Use integers or fractions for any numbers in the expressions.)

C. There is no solution. The solution set is empty set∅.

Answer #1

Use Gaussian elimination to find the complete solution to the
following system of equations, or show that none exists.
{-x + y + z = -2
{-x + 5y -19z = -30
{ 7x - 5y - 17z = 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....

Use Gaussian elimination to find the complete solution to the
following system of equations, or show that none exists.
{5x + 17y + 7z = 14
{2x + 7y -5z = -3
{ x + 3y - 3z = 8
Find the row-echelon form of the matrix for the given system of
equations. (Do not include the vertical bar in the
augmentedmatrix.)
Select the correct choice below and, if necessary, fill in the
answer boxes to complete your choice.
A....

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 {(_,_,_,_)}

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...

Solve the system of equations.
4x-3y+z = 18
x+y = 7
Select the correct choice below and, if necessary, fill in the
answer boxes to complete your choice.
A. This system has exactly one solution. The solution is left
parenthesis nothing comma nothing comma nothing right parenthesis .
(Type integers or simplified fractions.)
B. This system has infinitely many solutions of the form left
parenthesis nothing comma nothing comma z right parenthesis , where
z is any real number. (Type...

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 using either Gaussian elimination with
back-substitution or Gauss-Jordan elimination.If the system has an
infinite number of solutions, express x, y, and
z in terms of the parameter t.)
3x + 3y + 9z = 6
x + y + 3z = 2
2x + 5y + 15z = 10
-x + 2y + 6z = 4
(x, y, z)
= ?

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

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

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