Section 1:

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist.

A is 21, and B is 12.

Section 2:

Fill in the blanks.

To find the product matrix AB, the number of _____ ( columns, elements, rows) of A must be the same as the number of _____(rows, columns, elements) of B.

Section 3:

An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3

units of copper, 2 units of zinc, and 1 unit of glass. Each resistor requires 3, 1, and 2 units of the three materials, and each computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with 1635 units of copper, 740 units of zinc, and 1105 units of glass? Solve this exercise by using the inverse of the coefficient matrix to solve a system of equations.

The company can make ___ here transistors, ___resistors, and ___ computer chips.

Section 4:

The input-output matrix for a simplified economy with just four sectors (natural resources, manufacturing, trade and services, and personal consumption) is given below. Suppose the demand (in millions of dollars) matrix is matrix D given below. Find the amount each sector should produce.

Natural

Resources

Manufacturing

Trade and Services

Personal

Consumption

D =

	451
	300
	126
	100

Natural Resources

0.1045

0.0427

0.0029

0.0031

Manufacturing

0.0827

0.1087

0.0584

0.0321

Trade and Services

0.0866

0.1019

0.2032

0.3556

Personal Consumption

0.6253

0.3448

0.6106

0.0798

Production levels of ___ units from natural resources, ___ units from manufacturing, ___ units from trade and services, and ___ units from personal consumption are needed.