Question

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

Answer #1

The given system of equations is 2x+y+z=-2…(1), 2x-y+3z=6 …(2) and3x-5y+4z=7…(3).

The augmented matrix of this linear system is A (say) =

2 |
1 |
1 |
-2 |

2 |
-1 |
3 |
6 |

3 |
-5 |
4 |
7 |

To solve the given system of equations, we will reduce A to its RREF as under:

Multiply the 1st row by ½

Add -2 times the 1st row to the 2nd row

Add -3 times the 1st row to the 3rd row

Multiply the 2nd row by -1/2

Add 13/2 times the 2nd row to the 3rd row

Multiply the 3rd row by -1/4

Add 1 times the 3rd row to the 2nd row

Add -1/2 times the 3rd row to the 1st row

Add -1/2 times the 2nd row to the 1st row

Then the RREF of A is

1 |
0 |
0 |
-3 |

0 |
1 |
0 |
0 |

0 |
0 |
1 |
4 |

This implies that the given system of equations has a unique solution x = -3, y = 0 and z = 4.

10) b

11) b

12) a

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

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

for 7-9 you will solve the following system of equation :
2x+3u+z=17 x-3y+2z=-8 5x-2y+3z=5 7) what is the solution for x? a)2
b)1 c)infinitely many solution d)no solution 8)what is the solution
for y? a)4 b)2 c)inifinitely many solutions d)no solution 9) what
is the solution for z? a)9 b)1 c)inifinitely many solutions d)no
solution

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

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).

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

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

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 =...

Choose the augmented matrix that can used to solve this system
of equations:
3x+4y+2z=1
-2x+9y-z=0
-5y+21z=12

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