Exam 2: Systems of Linear Equations and Matrices

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

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

Solve the system of linear equations using the Gauss-Jordan elimination method. If there is no solution, answer none. ​

Compute the product. ​

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​

A university admissions committee anticipates an enrollment of 8,000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix ​ ​ By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the School of Engineering according to the percentages that appear in the following matrix: ​ ​ Find the matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline.

Solve the system of linear equations using the Gauss-Jordan elimination method. If there is no solution, answer none. ​

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

Perform the indicated operations.

Perform the addition.

A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are parallel.

Solve the system of linear equations, using the Gauss-Jordan elimination method. If there is no solution, answer none. ​ ​ __________ ​ __________

Let . Find A^-1.

Solve the system of linear equations using the Gauss-Jordan elimination method. If there is no solution, answer none. ​

Find the transpose of the given matrix.

Write the augmented matrix corresponding to the given system of equations.

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 ​ $__________ million output of the third sector

Write the augmented matrix corresponding to the given system of equations.

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.