**Learning Goal: **I’m working on a algebra question and need an explanation and answer to help me learn.

1. Write the system of equations as an augmented matrix

6x−6y−4z=6

−x+y−3z=6

x−5y+4z=6

2. Write the system of equations as an augmented matrix

u − 3y = 100

n + 6y = 200

2u + n + y = 250

3.A system of equations was written as an augmented matrix where

The coefficients of the unknown variable aa were put in column 1

The coefficients of the unknown variable zz were put in column 2

The coefficients of the unknown variable cc were put in column 3

which was row reduced to:

1 0 0 2

0 1 0 3

0 0 1 −5

What is the solution to the original system of equations?

z=

a=

c=

4. A system of equations was written as an augmented matrix where

the coefficients of the unknown variable rr were put in column 1

the coefficients of the unknown variable mm were put in column 2

the coefficients of the unknown variable ss were put in column 3

which was row reduced to:

1 0 0 −4

0 1 0 4

0 0 1 −1

What is the solution to the original system of equations?

r=

m=

s=

5. Write the system of equations as an augmented matrix

a + 3y =150

a + y + x =250

−a − 6y + x =200

[◻ ◻ ◻◻ ]

[◻ ◻ ◻◻ ]

[◻ ◻ ◻◻ ]

6. A system of equations was written as an augmented matrix, which was row reduced to:

1 0 0 −1

0 1 0 −6

0 0 1 −2

What is the solution to the original system of equations?

y=

x=

z=

7. Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter *z*.

{15x + 5y + z = −75

18x + 5y + 3z = −94

6x + 2y + z = −33

x=

y=

z=

8. Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter *z*.

8x + 3y + 15z = −38

12x + 6y + 18z = −60

4x + 3y + 3z = −22

x=

y=

z=

9. Write the augmented matrix as a system of equations

[0 2 1 250

0 1 0 400

−1 −3 1 100]

___ x+ ___y+ ___z= ___

___x+ ___y+ ___z= ___

___x+ ___y+ ___ z= ___

10. Let

M= [ 1 4 -2

5 -3 3]

[____ ____ ____

____ ____ ____]

11. Given A= [2 -1 -7 Given A= [250

-1 1 6 400

-1 -1 -5] 150]

Solve the matrix equation Ax=bAx=b for xx

x= =

[ ___

___

___]

12. Write out the matrix equation for this given system of equations

z + 2x = 200

−3z + y − 5x = 300

3z + 7x = 150

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