Question

Solve each system of equations

x-2y+3z=7

2x+y+z=4

-3x+2y-2z=-10

Answer #1

x-2y+3z=7

2x+y+z=4

-3x+2y-2z=-10

augmented matrix is

1 | -2 | 3 | 7 |

2 | 1 | 1 | 4 |

-3 | 2 | -2 | -10 |

convert into Add (-2 * row1) to row2

1 | -2 | 3 | 7 |

0 | 5 | -5 | -10 |

-3 | 2 | -2 | -10 |

Add (3 * row1) to row3

1 | -2 | 3 | 7 |

0 | 5 | -5 | -10 |

0 | -4 | 7 | 11 |

Divide row2 by 5

1 | -2 | 3 | 7 |

0 | 1 | -1 | -2 |

0 | -4 | 7 | 11 |

Add (4 * row2) to row3

1 | -2 | 3 | 7 |

0 | 1 | -1 | -2 |

0 | 0 | 3 | 3 |

Divide row3 by 3

1 | -2 | 3 | 7 |

0 | 1 | -1 | -2 |

0 | 0 | 1 | 1 |

Add (1 * row3) to row2

1 | -2 | 3 | 7 |

0 | 1 | 0 | -1 |

0 | 0 | 1 | 1 |

Add (-3 * row3) to row1

1 | -2 | 0 | 4 |

0 | 1 | 0 | -1 |

0 | 0 | 1 | 1 |

Add (2 * row2) to row1

1 | 0 | 0 | 2 |

0 | 1 | 0 | -1 |

0 | 0 | 1 | 1 |

solution is

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

Solve the following system of equations.
{−x+4y−z=-4
3x−y+2z=6
2x−3y+3z=−2
Give your answer as an ordered triple
(x,y,z).

Solve the system using 3x3
3x-2y+z=2
5x+y-2z=1
4x-3y+3z=7

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)

#7 Solve for x, y and z
6x+3y+z=-27
x-3y+2z+10
17x-2y+3z=-65

Solve the system of equations given below. 2x+5y+z= -1, 3x-5y-z=
6, 5x+y+3z= 10.

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

Consider the following linear system:
x + 2y + 3z = 6
2x - 3y + 2z = 14
3x + y - z = -2
Use Gaussian Elimination with Partial Pivoting to
solve a solution in an approximated sense.

Solve the system of equations using an inverse matrix
-4x-2y+z= 6
-x-y-2z= -3
2x+3y-z= -4
Choose one:
a. (-1, 0, -2)
b. (1, 0, -2)
c. (1, 0, 2)
d. (-1, 0, 2)

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]

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