Question

Solve the system. If there's no unique solution, label the system as either dependent or incomsistent.

2x+y+3z=12

x-y+4z=5

-4x+4y-4z=-20

a. Dependent system

b. inconsistent system

c.(1,4,2)

d. (4,1,2)

Answer #1

system is

augmented matrix is

2 | 1 | 3 | 12 |

1 | -1 | 4 | 5 |

-4 | 4 | -4 | -20 |

convert into Reduced Row Eschelon Form...

Divide row1 by 2

1 | 1/2 | 3/2 | 6 |

1 | -1 | 4 | 5 |

-4 | 4 | -4 | -20 |

Add (-1 * row1) to row2

1 | 1/2 | 3/2 | 6 |

0 | -3/2 | 5/2 | -1 |

-4 | 4 | -4 | -20 |

Add (4 * row1) to row3

1 | 1/2 | 3/2 | 6 |

0 | -3/2 | 5/2 | -1 |

0 | 6 | 2 | 4 |

Divide row2 by -3/2

1 | 1/2 | 3/2 | 6 |

0 | 1 | -5/3 | 2/3 |

0 | 6 | 2 | 4 |

Add (-6 * row2) to row3

1 | 1/2 | 3/2 | 6 |

0 | 1 | -5/3 | 2/3 |

0 | 0 | 12 | 0 |

Divide row3 by 12

1 | 1/2 | 3/2 | 6 |

0 | 1 | -5/3 | 2/3 |

0 | 0 | 1 | 0 |

Add (5/3 * row3) to row2

1 | 1/2 | 3/2 | 6 |

0 | 1 | 0 | 2/3 |

0 | 0 | 1 | 0 |

Add (-3/2 * row3) to row1

1 | 1/2 | 0 | 6 |

0 | 1 | 0 | 2/3 |

0 | 0 | 1 | 0 |

Add (-1/2 * row2) to row1

1 | 0 | 0 | 17/3 |

0 | 1 | 0 | 2/3 |

0 | 0 | 1 | 0 |

reduced system is

solution is

Solve each system by elimination.
1) -x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20
2) -4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4
3) -x-5y+z=17
-5x-5y+5z=5
2x+5y-3z=-10
4) 4x+4y+z=24
2x-4y+z=0
5x-4y-5z=12
5) 4r-4s+4t=-4
4r+s-2t=5
-3r-3s-4t=-16
6) x-6y+4z=-12
x+y-4z=12
2x+2y+5z=-15

Solve the following system of equations using matrices(row
operations). If the system has no solution, say that it is
inconsistent.
x + 6y+ 3z = 1
3x - 3y + 3z = 3
4x + 3y + 4z = 4

4. Solve the system of equations.
2x – y + z = –7
x – 3y + 4z = –19
–x + 4y – 3z = 18.
A. There is one solution (–1, –2, –3).
B. There is one solution (1, 2, 3).
C. There is one solution (–1, 2, –3).
D. There is one solution (1, –2, 3).

Solve the system using Gaussian elimination. State whether the
system is? independent, dependent, or inconsistent.
3x-y+2z=5
x+y-4z=6

for 10-12 you will solve the following system of equations:
2x+y+z=-2 2x-y+3z=6 3x-5y+4z=7 10) what is the solution for x? a)2
b)-3 c)infinitely many solutions d)no solution 11) what is the
solution for y? a)2 b)0 c)inifinitely many solution d)no solution
12) what is the solution for z? a)4 b)-8 c)infinitely many
solutions d)no solutions

BY USING SUBSTITUTION OR ELIMINATION, which of the following
systems are linearly dependent and which are inconsistent?
a.
2x + y - z = 10
4y + 2z = 4
x = 0
b.
-y + z = 0
4x + 2y - z/3 = 0
x + z = 0
c.
-3x + 2y - z = 14
-x - y - z = 0
x + 10y - 3z = 2

In Problems 17-20 use determinants to decide whether the system
has (a) a unique solution or (b) either no solution or infinitely
many solutions. Do not solve the system.
17. 3x − 4y = 7
x + 2y = -4
20. 4u + 2v + 4w = 2
2u + v + 2w = 1
3u - 4v + w = -5

Which of the following systems of equations have nonzero
solutions? If the solution is not unique, give the set of all
possible solutions.
a)3x+4y=0 b)4x-y=0 c)2x-6y=0
6x+2y=0 4x-y=0 -x+3y=-2

For a real number "a", consider the system of equations:
x+y+z=2
2x+3y+3z=4
2x+3y+(a^2-1)z=a+2
Which of the following statements is true?
A. If a= 3 then the system is inconsistent.
B. If a= 1 then the system has infinitely many solutions.
C. If a=−1 then the system has at least two distinct
solutions.
D. If a= 2 then the system has a unique solution.
E. If a=−2 then the system is inconsistent.

solve the following system and classify it consistent
or inconsistent
×+3y+3z=8
x-y+3z=4
2x+6y+6z=16

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