Question

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

Answer #1

construct a marix

2 | 1 | -1 | 7 |

1 | 2 | 1 | 8 |

1 | -2 | 3 | 2 |

Divide row1 by 2

1 | 1/2 | -1/2 | 7/2 |

1 | 2 | 1 | 8 |

1 | -2 | 3 | 2 |

Add (-1 * row1) to row2

1 | 1/2 | -1/2 | 7/2 |

0 | 3/2 | 3/2 | 9/2 |

1 | -2 | 3 | 2 |

Add (-1 * row1) to row3

1 | 1/2 | -1/2 | 7/2 |

0 | 3/2 | 3/2 | 9/2 |

0 | -5/2 | 7/2 | -3/2 |

Divide row2 by 3/2

1 | 1/2 | -1/2 | 7/2 |

0 | 1 | 1 | 3 |

0 | -5/2 | 7/2 | -3/2 |

Add (5/2 * row2) to row3

1 | 1/2 | -1/2 | 7/2 |

0 | 1 | 1 | 3 |

0 | 0 | 6 | 6 |

Divide row3 by 6

1 | 1/2 | -1/2 | 7/2 |

0 | 1 | 1 | 3 |

0 | 0 | 1 | 1 |

Add (-1 * row3) to row2

1 | 1/2 | -1/2 | 7/2 |

0 | 1 | 0 | 2 |

0 | 0 | 1 | 1 |

Add (1/2 * row3) to row1

1 | 1/2 | 0 | 4 |

0 | 1 | 0 | 2 |

0 | 0 | 1 | 1 |

Add (-1/2 * row2) to row1

1 | 0 | 0 | 3 |

0 | 1 | 0 | 2 |

0 | 0 | 1 | 1 |

solution is

Solve using elimination method:
x-2y+3z =4
2x-y+z = -1
4x + y + z = 5
What is z in the solution?

Solve each system of equations
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10

3) For the given system of equations:
x+y-z=-6
x+2y+3z=-10
2x-y-13z=3
Rewrite the system as an augmented matrix. [4 pt]
Find the reduced row echelon form of the matrix using your
calculator, and write it in the spacebelow. [4 pt]
State the solution(s) of the system of equations. [3 pt]

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

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

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...

1. Solve by via Gauss-Jordan elimination:
a) 2y + 3z = 8
2x + 3y + z =
5
x − y − 2z =
−5
b) x + 3y + 2z = 5
x −
y + 3z = 3
3x + y + 8z = 10
c) 3x1 + x2 + x3 + 6x4 = 14
x1 − 2x2 +
5x3 − 5x4 = −7
4x1 + x2 + 2x3 + 7x4 =
17

Use Gauss-Jordan Elimination to solve the following system of
equations. Please show all the wotk identifying what row operations
you are doing in each step
2x-4y+6z-8w=-10
x-2y+z+w=2
-2x+4y+z+2w=-3
-x+3y-3z+5w=6

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) (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 =...

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