Download Algebra 2 Chapter 4 Review

Algebra 2 Chapter 4 Review
Name:______________________
Date:_________ Period:_______
Section 4.1
1.) State the dimensions of 7 8 9 10 .
4 x  3 3 y  9  15 
2.) Solve 

13  7 2 z  1
 7
 4 x  11  3 y 
3.) Solve 


 y  1  x 
Section 4.2
4 6
4.)  1    5  ?
 3  8 
  5 7   4 0  2
5.) 

?
 6 8  9 0 1 
 1    4   3
6.) 5  1  6 3   2 8   ?
     
 3  5   4
7.)
1 4 6 2 9 27

?
2 3 0 3 0 3 
Section 4.3
8.) Fill in the blanks: A___ x ___ • B
3 x ___
= C 1x5
Write your answer as “blank 1, blank 2, blank 3”.
Multiply by hand. No graphing calculator.
 3 5
9.) 3  5  
?
  2 0
5
10.)    3  1 4  ?
8
5  2  1  4 2
11.) 

?
3   1 0
8 0
Section 4.4
12.) Translate  ABC where A(3, 2), B(4, -2), C(2, -1) 4 units up and 3 units left. What is
the translation matrix?
13.) Referring to #12, what are the coordinates of A’, B’ and C’?
14.) Referring to #12, what would the coordinates of A’, B’, and C’ be if you dilate  ABC
such that the perimeter is tripled? (Show set up)
15.) Referring to #12, what would the coordinates of A’, B’, and C’ be if you rotate  ABC
270 degrees. You do not have to memorize the rotation and reflection matrices!! 
Section 4.5
16.) Find the determinant of the 3x3 by hand (no graphing calc).
3 1 2
0 6 4
2 5 1
17.) Find the determinant of the 2x2 by hand (no graphing calc).
2 1
3
5
Section 4.7
0 1
 1 1
18.) Are P = 
and Q = 
 inverses?

 1 0
1 1
1 2 
19.) Find the inverse of 
 without using your calculator.
2 1 
6 3 
20.) Find the inverse of 
 without using your calculator.
8 4
Section 4.8
21.) Write the following system of equations as a matrix equation.
3x – y = 0
x + 2y = -21
22.) Write the matrix equation as a system of equations.
2  2  x   1
5 3    y    3 

    
23.) Solve the system of equations using a matrix equation and inverses. (Show all work - No
graphing calculator)
5x + 9y = -28
2x – y = -2
24.) Solve the system of equations using a matrix equation and inverses. You may use a
calculator to solve.
4x – 3z = -23
-2x – 5y + z = -9
y–z=3
How do you catch a UNIQUE Rabbit?
____ ____ ____ ____ ____ ____
5
18
9
14
11
2
  13
(z)   3 
 23 
(j) (0, 6), (1, 2), (-1, 3)
 10 
(f)   4
 
 5 
____ ____
20
23
____ ____
7
18
(y) (2, -3), (-2, -4), (-1, -2)
(u) No Solution
(w) 1, 3, 5
(e) (3, -5, 6)
(q) (9, 6), (12, -6), (6, -3)
(d) (14, 15)
1 2 

3
(k)  3
2  1


3
3
(r) 13
(n) Yes
(p) (-2, -2)
3  1  x   0 
(t) 
   

1 2   y   21
(i) 19 15
(a) 1 x 4
 4  15
(o)  3

 2  2 
(l) -58
(s) 2x – 2y = -1
5x + 3y = 3
 3  3  3
(h) 
4
4 
4
15  5 20
(g) 

24  8 32
____ ____
9
21