Exam 2: Systems of Linear Equations and Matrices

K & R builders build three models of houses, M1, M2, and M3, in three subdivisions I, II, and III located in three different areas of a city. The prices of the homes (in thousands of dollars) are given in matrix A: K & R Builders has decided to raise the price of each house by 3% next year. Write a matrix B giving the new prices of the houses.

Compute the product. ​

Solve the matrix equation for the given matrices A, D and X. Round the elements of X to two decimal places.

Compute the product. ​ ​

The annual interest on Sid Carrington's three investments amounted to $18,200: 4% on a savings account, 6% on mutual funds, and 8% on bonds. If the amount of Sid's investment in bonds was triple the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds, find how much money he placed in each type of investment. $__________ in a savings account $__________ in mutual funds $__________ in bonds

Solve the system of linear equations using the Gauss-Jordan elimination method.

Pivot the system about the bolded element.

Solve the system of linear equations, using the Gauss-Jordan elimination method.

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met. ​ ​ Round each answer to two decimal places, if necessary. ​ $__________ million output of the first sector ​ $__________ million output of the second sector

Indicate whether the matrix is in row-reduced form. Answer yes or no. ​

Compute the product. ​ ​

Matrix A gives the percentage of eligible voters in the city of Newton, classified according to party affiliation and age group. ​ ​ The population of eligible voters in the city by age group is given by the matrix B: ​ ​ Find a matrix giving the total number of eligible voters in the city who will vote Democratic, Republican, and Independent.

Find the transpose of the given matrix.

Find the sizes of A, B,C and D.

Determine whether the statement is true or false. ​ A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel.

Find the inverse of the given matrix, if it exists. If not, write does not exist. Verify your answer. ​

Solve for u, x, y, and z in the matrix equation.

Indicate whether the matrix is in row-reduced form.

A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.1 unit of agricultural products and 0.1 unit of manufactured goods. The production of 1 unit of manufactured products requires the consumption of 0.1 unit of agricultural products and 0.4 unit of manufactured goods. Find the gross output of goods needed to satisfy a consumer demand for $140 million worth of agricultural products and $140 million worth of manufactured products. Round answers to the nearest tenth, if necessary. ​

Perform the indicated operations.