Download 1. Solve using row operations (augmented matrix). 3x + 4y = 10 x

COLLEGE ALGEBRA II (MATH 010)
SPRING 2017
PRACTICE FOR EXAM III
1. Solve using row operations (augmented matrix).



3x + 4y = 10
x − 4y = −2
2. Solve each system (aug. matrix), 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
3. Solve the system using row operations (augmented
matrix).



x − 2y + z = 1


y + 2z = 5



 x +
y + 3z = 8
4. Solve the system using row operations (augmented
matrix).
(a)









x + y + z = 2
y − 3z = 1
2x + y + 5z = 0
1
(b)









2x − 3y − 9z = −5
x
+ 3z = 2
−3x + y − 4z = −3
5. Perform the indicated operation, if possible.

A=
D=

H=
(a) AD
(b) DA

2 −5
0 7
7 3

3 1 1
2 −1 0
(c) AH


(d) HA
6. For the following system:
(a) Write as a matrix equation.
(b) Calculate the determinant of the coefficient matrix.
(c) Does the coefficient matrix have an inverse? Explain briefly.









x + y + z = 6
2x − y − z = 3
x + 2y + 2z = 0
7. Solve the system by converting to a matrix equation
and using the inverse of the coefficient matrix.



x − 4y = −2
−2x + y = −3
2
8. Solve using Cramer’s Rule.



x + 2y = 7
5x − y = 2
9. Solve using Cramer’s Rule.









x − y + 2z = 7
3x
+ z = 11
−x + 2y
= 0
10. Find the inverse of A if it exists.



A=

2 4 1
−1 1 −1
1 4 0
3




