Math 11AD

Operations with Matrices

1. a) State the dimensions of the following matrices:

b) For the above matrices, find the indicated elements:

c) For the above matrices transpose:

2. Perform the indicated operations.

a) b)

c) d) e)

3. Given: Find:

a) b) c) d) e) f) g)

4. Given that A: = B = C = D = E =

F = G = H = … complete all of the following operations OR solve for the unknown matrix (X).

a) A+B b) AE c) EA d) GH e) HG f ) FH g) HF

Solve… h) ½ C – 4X = GT i) X2 + 3DX - 4D = 0

5. Solve each equation for the 2 × 2 matrix.

a) b) c)

d) e)

6. State the values of the unknowns.

a) b) c)

Matrix Multiplication word problems

1. An investor plans to buy 100 shares of telephone stock, 200 shares of oil stock, 400 shares of automobile stock, and 100 shares of airline stock. The telephone stocks sells for $46 a share, the oil stock for $34 a share, the automobile stock for $15 a share and the airline stock for $10 a share.

a) Express the number of shares as a row vector (matrix).

b) Express the prices of the stocks as a column vector.

c) Use matrix multiplication to compute the total cost of the investor’s purchases.

2. 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 a 2 x 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.

3. A family consists of 2 adults, 1 teenager, and 3 young children. Each adult consumes 1/5 loaf of bread, no milk, 1/10 pound of coffee, and 1/8 pound of cheese in a an average day. The teenager eats 2/5 loaf of bread, drinks one quart of milk, but no coffee, and eats 1/8 pound of cheese. Each child eats 1/5 loaf of bread, drinks ½ quart of milk, but no coffee, and eats 1/16 pound of cheese.

a) Express the daily consumption of bread, milk, coffee, and cheese by the various types of family members using a matrix.

b) Express the number of family members of the various types by a column matrix.

c) Use matrix multiplication to calculate the total amounts of bread, milk, coffee, and cheese consumed by this family in an average day.

Answers: TBA

1. a) 2x2 3x1 1x4 3x4

b) 4 no solution -3 -2

c)

2. a) b) c) d) e) no solution

3. a) b) c) no solution d)

e) f) g)

4. a) no solution b) c) d)

e) f) no solution g) h) X=

i) X= or =

5. a) b) c) d)

e)

6. a) b) c)

Word Problems

1. a) b) c) $18400

2. a) b) c)

3. a) b) c)