Exam 3: Matrices

Set up the system of equations and then solve it by using inverse matrices. ​ Nutrition A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centimeters of each solution should be mixed to obtain 35 cc of a 28% solution? ​

A primitive economy has a mining industry and a fishing industry, with technology matrix A. ​ ​ ​ If surpluses of 132 units of mining output and 27 units of fishing output are desired, find the gross production of each industry. ​

A system of linear equations and a reduced matrix for the system are given. Use the reduced matrix to find the general solution of the ​ System, if one exists. ​

Matrix A below gives the fraction of the Earth's area and the projected fraction of its population for five continents in 2050. Matrix B gives the Earth's area (in square miles) and its projected 2050 population. Find the area and population of each given continent by finding AB. ​ ​ , ​

Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The matrix below gives the amounts of debt and the terms for the companies being purchased. Suppose ALCO decides to pay 80% of all debts due in 30 days and to increase the debts due in 60 days by 20%. Write a matrix that gives the debts after these transactions are made. ​ ​ ​

The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and food; RM, raw materials; M, manufacturing; F, fuels industry; U, utilities; SI, service industries) ​ ​ Which industry would be most affected by a rise in the cost of utilites? ​

Use the matrices to find , if possible. ​ ​

Use technology to solve the system of equations, if a solution exists.

Use the matrices below. Perform the indicated operations. AI ​

Find x, y, z and w. ​ ​

Use the indicated row operation to change matrix A, where . ​ Add times row 1 to row 3 of matrix A and place the result in row 3 to get 0 in row 3, column 1. ​

(CD)·E and C·(DE) are equal. ​

Use a graphing calculator to find the inverse of . ​

Use the matrices below. Perform the indicated operations. ​ IA

Use row operations on the augmented matrix to solve the given system of linear equations. ​ ​

Use technology to solve the system of equations, if a solution exists. ​

For , what size is each product FFT and F^TF? ​​

A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio III consists of 7 blocks of common stock, 3 municipal bonds, and 3 blocks of preferred stock. A customer wants blocks of common stock, municipal bonds, and blocks of preferred stock. How many units of each portfolio should be offered? ​

The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars. Which type of pollution abatement was most expensive in 2005? ​

A system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the following system, if a solution exists.