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Algebra 2
Unit: Systems of Equations and Inequalities
Section: Matrices and Determinants
Review Worksheet
1) Organize the following data into a matrix:
Sue
Joe
Number of Peak Minutes Used
251
402
Number of Off Peak Minutes Used
337
107
2) Use the following matrices to perform the given operations.
⎡ 1 −7 ⎤
A=⎢
⎥
⎣0 4 ⎦
a. A + B
b. B – A
c. A + C
d. 3C
e. AB
f. BC
2⎤
⎡6
B=⎢
⎥
⎣ −9 −3 ⎦
⎡3 −2⎤
⎢
⎥
C = ⎢0 4 ⎥
⎢⎣5 11⎥⎦
⎡ 5 −2 3 ⎤
D=⎢
⎥
⎣ 1 −5 0 ⎦
g. AD
h. Find the determinant of A. Does this matrix have an inverse?
i. Find the determinant of B. Does this matrix have an inverse?
Algebra
Writing Assignment: Matrices
Each problem is worth 5 points
Answer each of the following problems. Show all your work.
⎡2 3⎤ ⎡− 1 7 ⎤
1) Evaluate ⎢
⎥+⎢
⎥.
⎣5 1⎦ ⎣ 9 8 ⎦
⎡6 10 ⎤ ⎡ 1
⎥ ⎢
⎢
2 0⎥ ⎢ 5
2) Evaluate ⎢
−
⎢0 5 ⎥ ⎢ 1
⎥ ⎢
⎢
⎣ 1 7 ⎦ ⎣− 10
9⎤
⎥
9⎥
.
3⎥
⎥
0⎦
⎡2 4 ⎤ ⎡ 1⎤
3) Evaluate ⎢
⎥+⎢ ⎥.
⎣ 1 − 6⎦ ⎣0⎦
4) Evaluate 5[1 9 2 − 6] .
⎡6 2 ⎤
⎡ 1 5⎤
5) Evaluate 2 ⎢
⎥.
⎥ − 5⎢
⎣ 1 8⎦
⎣6 0 ⎦
6) Is the following operation possible? Why or why not?
⎡ 1 2⎤ ⎡ 1⎤
⎥⎢ ⎥
⎢
⎣3 7 ⎦ ⎣5 ⎦
7) Is the following operation possible? Why or why not?
[5
⎡2⎤
6 0]⎢ ⎥
⎣− 1⎦
⎡ 1 − 6⎤ ⎡ 1 4⎤
8) Evaluate ⎢
⎥.
⎥⎢
⎣2 0 ⎦ ⎣9 8 ⎦
⎡ 1⎤
⎢ ⎥
9) Evaluate ⎢7⎥[2 − 1 5] .
⎢⎣3⎥⎦
⎡5 6 ⎤
10) What is the determinant of ⎢
⎥?
⎣1 9⎦
Algebra 2
Writing Assignment: Systems of Equations
Each problem is worth 5 Points
Total Points: 50
Solve each system of equations. Show your work.
1. -2x + 3y = 8
3x – y = -5
2. 4x - y = 8
-8x + 2y = -5
3. 5x + y = 13
3x = 15 – 3y
4. 2x + 4y = 36
10y = 5
5. 2x – 4y = 12
3x – 6y = 21
6. 2x – 9y = 32
4x + y = -12
7. y = 3x + 1
4y = 12x + 4
8. –x + 2y = -4
2x – 3y = 8
9. 2x – 5y = -3
-x + 2y = 3
10. 3x + 4y =8
-2x + 5y = 3
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