Question

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*,

Answer #1

Augmented matrix for given system of equations

Your matrix

X1 | X2 | X3 | b | |
---|---|---|---|---|

1 | 3 | 3 | 9 | 6 |

2 | 1 | 1 | 3 | 2 |

3 | 2 | 5 | 15 | 10 |

4 | -1 | 2 | 6 | 4 |

Find the pivot in the 1st column and swap the 2nd and the 1st rows

X1 | X2 | X3 | b | |
---|---|---|---|---|

1 | 1 | 1 | 3 | 2 |

2 | 3 | 3 | 9 | 6 |

3 | 2 | 5 | 15 | 10 |

4 | -1 | 2 | 6 | 4 |

Eliminate the 1st column

X1 | X2 | X3 | b | |
---|---|---|---|---|

1 | 1 | 1 | 3 | 2 |

2 | 0 | 0 | 0 | 0 |

3 | 0 | 3 | 9 | 6 |

4 | 0 | 3 | 9 | 6 |

Make the pivot in the 2nd column by dividing the 3rd row by 3 and swap the 3rd and the 2nd rows

X1 | X2 | X3 | b | |
---|---|---|---|---|

1 | 1 | 1 | 3 | 2 |

2 | 0 | 1 | 3 | 2 |

3 | 0 | 0 | 0 | 0 |

4 | 0 | 3 | 9 | 6 |

Eliminate the 2nd column

X1 | X2 | X3 | b | |
---|---|---|---|---|

1 | 1 | 0 | 0 | 0 |

2 | 0 | 1 | 3 | 2 |

3 | 0 | 0 | 0 | 0 |

4 | 0 | 0 | 0 | 0 |

Solution set:

x = 0

y = 2 - 3t

z = t, t = free parameter

(x,y,z) = (0, 2 - 3t, t) (answer)

Solve the system using either Gaussian elimination with
back-substitution or Gauss-Jordan elimination. (If there is no
solution, enter NO SOLUTION. If the system has an infinite number
of solutions, express x1,
x2, and x3 in terms of the
parameter t.)
2x1
+
3x3
=
3
4x1
−
3x2
+
7x3
=
4
8x1
−
9x2
+
15x3
=
13
(x1,
x2, x3) =
()

Solve the system using either Gaussian elimination with
back-substitution or Gauss-Jordan elimination.If the system has an
infinite number of solutions, express x1,
x2, and x3 in terms of the
parameter t.)
2x1 + 3x3 =
3
4x1 - 3x2
+ 7x3 = 1
8x1 - 9x2
+ 15x3 = 11
(x1,
x2, x3) =
?

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

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...

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

Use either Gaussian Elimination with back substituting or
Gauss-Jordan Elimination to solve the system:
−?1 + ?2 + 2?3 = 1 2?1 + 3?2 + ?3 = −2 5?1 + 4?2 + 2?3 = 4

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

Solve the system of linear equations using the Gauss-Jordan
elimination method.
2x
+
2y
+
z
=
7
x
+
z
=
2
4y
−
3z
=
21

3x+2y=2,6x+4y=1, 5y+z=-1 solve system of eq using gauss jordan or
gauss elimination

Use Gauss-Jordan Elimination to solve the following system of
equations.
−4x
+
8y
+
4z
= −4
−3x
+
6y
+
3z
= −3
x
−
2y
−
z
= 1

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 36 minutes ago

asked 37 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago