Texts: 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 2×1, and B is 1×2.
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 ___ 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 0.10 450 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.