Name: __________________________________________________________________ Per __________ Algebra II Matrices HW
ALL WORK ON SEPARATE PAPER- Label with date and Section!
I.
Solve by Substitution
1.
II.
2 x y 4 z 8
3x 2 y 1
x y 1
2.
Solve by Elimination
5 x 3 y 2 z 1
1. 2 x y z 1
2 x 2 y z 2
4 x 2 z 14
y x z 12
2 x 4 z 22
x y 2 z 7
2. 2 x 3 y z 1
3x 4 y z 4
For Parts III. – V. Use the following matrices. Show all work. (ENTER ALL MATRICES FIRST!)
A=
6 2
1 5
.25 .25
F=
8
16
III.
B=
4 0
7 5
C=
5.7 1.6
G=
2
3.2
3 0
14 2
E=
4 .5
1 2
0 11
10
J= 7 1 9
I = 2
3
1
3 0 1
5 25 4
3 1
11 3
D=
0 1 2
H=
1 3 2
2 8 3
Determine the order (dimensions) of each matrix.
A______, B______, C______, D_______, E______, F______, G______, H______, I_______, J_______
IV.
Find the determinant.
1.
V.
det A=_____
2.
|B| =_____
3.
|H|=______
4.
det J=_____
2.
[B]-1 =
3.
[H]-1 =
4.
[J]-1 =
Find the inverse.
1.
VI.
[A]-1 =
Determine if the following matrices have an inverse. If yes, find the inverse.
1.
2.
VII.
VIII.
3 4
-1
2 5 Yes or No A = ______
4 10
B=
Yes or No B-1 = ______
2 5
A=
3.
4.
1
1
0
D=
4
C=
1
Yes or No C-1 = ______
1
3 1
Yes or No D-1 = ______
1 0
Perform the operation. # 1-3 ALL and #4-9 *Pre AP Only*
1.
AG
4.
D–H
7.
-2C
2.
HI
5.
A+D
8.
2A + 3D
3.
CI
6.
E–F
9.
3C – 2A
Solve for x and y.
1.
4x
17 24 17
y 2 42 15 42
2.
16 5x 16 20
7y 13 21 13
3.
2 x y 16 3
5
4 5 4
Created by Shirly Boots @ www.EverythingAlgebra.com
4.
.5 3 y .5 3
.5 x
4 5 4
5.
**PAP
6.
**PAP
5 x 7 y 3 13 10
4 2 x 13 y 9 7
4 5 y
6 10 10
3 x 5
7
x 1 7 3 y 1 14 9
IX.
1.
Solve
x y 5
2 x y 6
2.
4 x 7 y 10
3x 5 y 9
3.
3x y 5
y 2x 4
4.
x y z 0
2x y 2z 8
x 4z 10
5.
3x 3 y z 19
5x 4 y 2z 28
2x 2y z 12
6.
x y z 10
2 x z 12
z y 3
X.
7.
2 x 2 y z 6
3x 2 y 2 z 8.48
4 x 3 y 2 z 10.46
8.
2 x y 3 z 2365
x 3 y 2 z 2045
3x 2 y z 2460
w 5 x 2 y z 18
3w x 3 y 2 z 17
9. **PAP
4w 2 x y z 1
2w 3x y 4 z 11
2w x 5 y z 3
3w 2 x 2 y 6 z 32
10. **PAP
w 3x 3 y z 47
5w 2 x 3 y 3 z 49
Write and solve systems of equations.
1.
Gerardo bought some neon fish at $2 each and some angel fish at $3 each for his new aquarium. Cory bought a total of 20 fish
and spent $45. How many of each fish did he buy?
2.
John inherited $25,000 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund.
After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually,
the bonds paid 7% annually, and the mutually fund paid 8% annually. There was $6,000 more invested in the bonds than the
mutual funds. Find the amount John invested in each category.
3.
An ice cream stand sells chocolate, strawberry, and vanilla ice cream. Yesterday they sold a total of 232 ice creams. The
number of strawberry is equal to 4 fewer than 3 times the number of vanilla. The number of strawberry and vanilla combined
equals the number of chocolates sold. How many of each did they sell?
4.
Juan’s taco Hut sells tacos, burritos and enchalladas. Yesterday they sold a total of 952 food items. The number of tacos they
sold was 12 less than 2 times the number of burritos. The number of enchalladas they sold was half the number of tacos sold.
What is the anount of each food item sold.
5.
A college entrance test consists of 112 questions. The test contains true/false (7 points each), fill-in-the-blank (9 points each),
and multiple choice (13 points each). There are 1172 possible points total on the test. The number of fill-in-the-blank is 34 less
than the number of true/false. How many points come from fill-in-the-blank questions?
6.
An architect is determining the rectangular dimensions of a room. The length measures 6 more than the width. The height is 8
feet less than the length. The sum of all three measures is 46. What are the measurements of the room?
7.
Eva had a bake sale to earn extra money. On the first day, she earned $6.25 selling 5 cookies and 2 brownies. On the second day,
she earned $7.75 selling 3 brownies and 4 pieces of pie. On the third day, she earned $6.00 selling 8 cookies. If Eva sold 6
cookies and 1 piece of pie the next day, how much did she make?
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