Vectors and Matrices 5, question homework help

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Name: Date: Graded Assignment Unit Test, Part 2: Vectors and Matrices Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. 1. The matrices show the numbers of different types and sizes of sweaters that a clothing store has in stock. Boys Girls Small Medium Large Small Medium Large Button 24 Zipper  32 11 8 16  14  Button  7 Zipper 32 15 9 26  21 (a) Add the matrices. Label the sum as matrix A. Describe what matrix A represents. (b) What does element a12 represent? (c) If you add all the elements in the second row of matrix A, what would this number represent? (d) How many large sweaters does the store have in stock? Tell how you can use matrix A to determine the answer. (e) Write a matrix that represents how many more girls than boys button and zipper sweaters the store has in stock in each size. Answer: 2. The first matrix shows the cost of two types of sweaters (in dollars) and the second shows the number of each type sold during different months. Cost Button Zipper 22 18  Nov. Dec. Jan. Feb. Button  5 Zipper 25 18 40 32 38 40  12 (a) Multiply the matrices. (b) How much more money was spent on sweaters sold in January than in December? Tell how to use your answer from Part (a) to answer this question. Answer: 4 x  3 y  4 3. Use Cramer’s rule to solve  . Show your work. 3 x  y  7 Answer: 4. A triangle has vertices  2, 3,  3,5, and (8,–1) . (a) Write a matrix expression to represent reflecting the triangle across the x-axis. Evaluate the matrix expression and list the coordinates of the vertices of the transformed figure. (b) Write a matrix expression to represent rotating the triangle 90° clockwise. Evaluate the matrix expression and list the coordinates of the vertices of the transformed figure. Answer:  x  2y  2 5. Solve  by writing and solving a matrix equation. Show all your work. 3 x  5 y  9 Answer:
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Name:

Date:

Graded Assignment
Unit Test, Part 2: Vectors and Matrices
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for
full credit.

1.

The matrices show the numbers of different types and sizes of sweaters that a clothing store has in stock.

Boys

Girls

Small Medium Large

Small Medium Large

Button 24
Zipper  32

11
8

16 
14 

Button  7
Zipper 32

15
9

26 
21

(a) Add the matrices. Label the sum as matrix A. Describe what matrix A represents.
(b) What does element a12 represent?
(c) If you add all the elements in the second row of matrix A, what would this number represent?
(d) How many large sweaters does the store have in stock? Tell how you can use matrix A to determine
the answer.
(e) Write a matrix that represents how many more girls than boys button and zipper sweaters the store
has in stock in each size.
Answer:
(a) Matrix A1 represents Boys
Matrix A2 represents Girls
𝐴 = 𝐴1 + 𝐴2
𝐴 =[

24
32

11
8

16 ] [ 7
+
14
32

15
9

26 ]
21

Small Medium Large

𝑨 =[

𝟑𝟏
𝟔𝟒

𝟐𝟔
𝟏𝟕

𝟒𝟐] Button
𝟑𝟓 Zipper

The result is matrix A that represents the total boys and girls sweaters sizes and types.
(b) If we see the matrix A, the element in the first row, second item denominated a 12 is 26, it represents
26 boys and girls sweaters, that have button and are of medium size.
(c) In the matrix A we have in the second row the zippered sweaters. If you add the values you will have
the total of all sizes of boys and girls sweaters that have zipper.
(d) If we see the matrix, we know that large size is in the third column with the values 42 and 35. Then
we can add them and have the total of large sweaters that is 77.
(e) We can make the same procedure for the question a but making the difference between matrix A1
and A2, then we obtain how many more girls than boys button and zipper sweaters the store has in
stock in each size.

𝐴 = 𝐴1 − 𝐴2

Small Medium Large

−𝟏𝟕
𝐀𝟑 = [
𝟎

+𝟒
+𝟏

+𝟏𝟎] Button
+𝟕
Zipper

With this result we obtain the matrix A3 that shows the amount of girl sweaters in stock. We can
observe that there are negative values that represents there are no more girl sweaters than boys in that
size ortype. Also we have positive values that indicate there are more girls sweaters than boys in that size
or type in the store.

2.

The first matrix shows the cost of two typ...


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