Peru State College Linear Algebra Matrices & Determinants Questions

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

Requirements: each problems
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This is a homework Q&A between a student and a tutor. If the final answer looks incomplete, expand the discussion to see if you can find what you’re looking for.
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

Requirements: each problems