Review Matrix
Page 1
Matrix
--------------------------------------------------------------------------------------1)
Find the determinants of the following matrices.
1.1)
2
A = 
1

4

3 
1.2)
 −1
B = 
 −2

0

3 
1.3)
3
C = 
4

−1

−1
1.4)
 −2
D = 
1

−1

3 
1.5)
1 2

E =  −1 3

2 1

1.6)
1

F = 2

0

4

0

1 
0
0
4
1

5

3 
Review Matrix
1.7)
2)
Page 2
2

G = 1

 −3

3

−1 2 

1 0 
2
1.8)
2

H = 0

1

5
−1
2
Find the value of x in each of the following.
2.1)
2.3)
1
2
x−2
3x
x−6
−3
−2
−1
0
1
x
3
x+2
= 4
2.2)
= 0
4x
−1
3
−x
= −1
1 

1 

−2 
Review Matrix
3)
Page 3
2
Given that A = 
3

3.1)
det(2A)
3.2)
det(B)
3.3)
det(Bt)
3.4)
det(AB)
3.5)
det(2B)
4
1
 and B = 
6
−1

−2 
 , find
−1 
Review Matrix
4)
Page 4
Solve each of the following systems of equations using the inverse matrix.
4.1)
2x – y = -3
3x + 4y = 12
4.2)
x – 3y = 4
-2x + 4y = 5
Review Matrix
5)
Page 5
Solve each of the following systems of equations using the Cramer’s rule.
5.1)
3x + y – 2z = -1
2x – 3y + z = 4
4x + 5y – z = -2
5.2)
x + 2y – 4z = 2
2x + 3y – 7z = 3
3x – y + 5z = 1
Review Matrix
6)
Solve the following systems of equations using the row operations.
x – 3y + z – 2w = 28
2x + y + 3z – w = 9
3x + 2y – z + w = 0
-x + y + 4z – 3w = -1
Page 6