A
B
C
| 3 1 2
|
|-2 1
|
|2 3 -2 |
| 7 5 6
|
| 3 -4 |
| -5 3 |
| 6 2 |
A: 2 x 3
B: 4 x 2
C: 1 x 3
2 | 3 4| = |
6
8|
| 5
1|
|10 2|
Subtract: | 3 -4 |
-
| -5 4 | = | 8 -8 |
| 1 5
|
| 3 -2 | | -2 7 |
Addition & Scalar Multiplication:
4 | 3 -1 2 | + 2 | -1 4 5 | - .5 |4
6 8 |
| 2 3 5 | |
-4 8
1|
|5 2 1|
= | 12 -4 8 | + |
-2 8 10 | - |
2
3 4 |
| 8 12 20|
| -8 16 2 | | 2.5
1 .5 |
= |10 4 18 | - |
2
3 4 |
| 0 28 22| |
2.5
1 .5 |
= | 8
1 14 |
| -2.5 27 21.5 |
| 3x - y | = | 1 |
| 2x + 3y| | 8 |
Solve the system:
3x - y = 1
2x + 3y = 8
Multiply the first equation by 3
and
add: 9x - 3y = 3
2x + 3y = 8
11x = 11
x = 1
Substitute x = 1 back into the
first
equation and solve for y: 3(1) - y = 1
3 - y = 1
- y = -2
y = 2
Example 2:
| 3x + y | = | x + 3 |
| x - 2y | |
y - 2 |
3x + y = x + 3
x - 2y = y - 2
2x + y = 3
x - 3y = -2
2x + y = 3
-2x + 6y = 4
7y = y
y = 1
x - 2(1) = 1 - 2
x - 2 = -1
x = 1
So the original matrix is | 4 |
| -1 |
Word Problem:
The juniors at Adams High School held a two-day bake sale to raise
money for a class trip. Cupcakes, cookies, and pies were sold for
$.40,
$.25, and $4.00 respectively. The first
day
84 cupcakes, 210 cookies, and 27
pies
were sold. The second day, 95 cupcakes,
184
cookies, and 17 pies were sold. Find the amount of
money raised each day and altogether.
cupcakes cookes
pies
cost
Cookies Matrix: Day 1
|
84
210
27 | Cost
Matrix:
cupcakes | .40 |
Day 2
|
95
184
17 |
cookies | .25 |
pies | 4.00
|
Multiply the cookies matrix by the cost matrix: | 194.10 |
| 152.00 |
Problems (there are no problems here yet)