Download 1. Solve using substitution. x - y = 1 4x + 3y = 18 2

COLLEGE ALGEBRA II (MATH 010)
FALL 2014
PRACTICE FOR EXAM II
1. Solve using substitution.



x − y = 1
4x + 3y = 18
2. Solve using elimination.



3x + 4y = 10
x − 4y = −2
3. Solve each system, or show that it has no solution.
If it has infinitely many solutions express them in
terms of a single parameter (t).
(a)



x + 4y = 8
3x + 12y = 2
(b)



2x − 6y = 10
−3x + 9y = −15
4. Solve the system, or show that it is inconsistent.









x −
y − z = 4
2y + z = −1
−x + y − 2z = 5
1
5. Solve the system, or show that it is inconsistent.
(a)





y − 2z = 0
2x + 3y
= 2
−x − 2y + z = −1




(b)









x + 2y − z = 1
2x + 3y − 4z = −3
3x + 6y − 3z = 4
6. Solve the system using row echelon operations (augmented matrix).









x − 2y + z = 1
y + 2z = 5
x + y + 3z = 8
7. Solve the system using row echelon operations (augmented matrix).
(a)









x + y + z = 2
y − 3z = 1
2x + y + 5z = 0
(b)









2x − 3y − 9z = −5
x
+ 3z = 2
−3x + y − 4z = −3
2
8. Perform the indicated operation, if possible.

A=
D=

H=
(a) AD
(b) DA

2 −5
0 7
7 3

3 1
2 −1


(c) AH
9. (a) Write as a matrix equation.
(b) Calculate the determinant of the coefficient matrix.
(c) Is the coefficient matrix invertible? Explain briefly.









x − 2y + z = 1
y + 2z = 5
x + y + 3z = 8
10. Solve the system by converting to a matrix equation
and using the inverse of the coefficient matrix.



x − 4y = −2
−2x + y = −3
11. Solve using Cramer’s Rule.



x + 2y = 7
5x − y = 2
12. Solve using Cramer’s Rule.









x − y + 2z = 7
3x
+ z = 11
−x + 2y
= 0
3
13. Use row operations to find
ing matrix.

2


−1
A=

1
4
the inverse of the follow4 1
1 −1
4 0




