Page 842 - Algebra 1

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Caution
Matrices can be added or subtracted only if they have the same number of rows and the same number of columns.
5. The element in the third row, second column is .
6. Describe the dimensions of a matrix representing data about a school
fundraiser with five types of items available in four different sizes.
Since matrices are a method of organizing information, sometimes they are added or subtracted to get new information. Matrices that have the same dimensions can be added subtracted.
The table shows the number of items sold during the second day of the fundraiser.
Items Sold on Second Day
Item Medium Large
T-shirts 8 3 Hats 1 5 Sweatshirts 4 7
7. Generalize Explain how to find the total number of large hats sold during the first two days of the fundraiser.
8. Formulate Explain how to use matrices to find the total number of large hats sold during the first two days of the fundraiser.
9. Use matrices to model the sum of the items sold during the first two days. Then add the matrices using a graphing calculator.
10. Find the difference between the two matrices. How many more medium hats were sold on the first day than on the second day?
Matrix addition also has a geometric application.
Exploration Using Matrix Addition to Transform Geometric Figures
Graphing Calculator Tip
For help with adding matrices, see the Graphing Calculator Lab 11 on page 824.
y
4 A 2
O
B -2 -4
3⎤ .
14. Use the elements of A + B as the coordinates of the vertices of △A'B'C'.
Plot the vertices of △A' B' C' to create a graph of the triangle.
15. Write Describe the relationship between △ABC and △A'B'C'.
16. What matrix would translate △ABC one unit to the left and three units down?
11. Complete the following table by finding the coordinates of the vertices of △ABC.
x-coordinate y-coordinate
-4
2
4
Point A -1
Point B -2 -1
Point C
x
C
-2 12. Use the data in the table to create matrix A.
13. Using a graphing calculator find the sum A + B, when B = ⎡⎢3
3
⎣2 2 2⎦
Investigation 12 827