Question

A company pays its executives a salary and gives them shares of its stock as an annual bonus. Last year the president of the company received $80,000 and 50 shares of stock, each of the three vice−presidents was paid $45,000 and 20 shares of stock, and the treasurer was paid $40,000 and 10 shares of stock. a. Express the payments to the executives in money and stock by means of a 2 × 3 matrix. b. Express the number of executives of each rank by means of a column vector. c. Use matrix multiplication to calculate the total amount of money and the total number of shares of stock the company paid these executives last year.

Answer 1

a. Payments to the executives can be expressed in a 2x3 matrix. b. The number of executives of each rank can be expressed in a column vector. c. The total amount of money and the total number of shares of stock paid to the executives can be calculated using matrix multiplication.

Step-by-step explanation:

a. Payments to the executives can be expressed in a 2x3 matrix where each row represents the payment in money and stock for a different executive. Let's call this matrix A. The first row of matrix A represents the president's payment, the second row represents the three vice-presidents' payments, and the third row represents the treasurer's payment. The first column represents the payment in money and the second column represents the payment in stock. So, matrix A is:

A =

| 80000 50 |

| 45000 20 |

| 40000 10 |

b. The number of executives of each rank can be expressed in a column vector. Let's call this vector B. The elements of vector B represent the number of executives at each rank, starting with the president and ending with the treasurer. So, vector B is:

B =

[1

3

1]

c. To calculate the total amount of money and the total number of shares of stock paid to the executives last year, we need to multiply matrix A by vector B using matrix multiplication. Let's call the result matrix C. The first element of matrix C represents the total amount of money paid, and the second element represents the total number of shares of stock paid. So, matrix C is:

C = A * B =

| 80000*1 + 45000*3 + 40000*1 50*1 + 20*3 + 10*1 |

|

80000 + 135000 + 40000

|

50 + 60 + 20

|

| 315000 130 |