Exam 1: Systems of Linear Equations

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Balance the given chemical equation.

Find the equilibrium temperatures for the heavy wires with endpoints held at the given temperatures.

Compute the first three Gauss-Seidel iterations for the system in question 5, using as the initial value for each variable. Then find the exact solution and compare.

Find all possible equilibrium and endpoint temperatures for the heavy wires with endpoints held at the indicated temperatures.

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Convert the given system to an augmented matrix, and find all solutions by reducing to echelon form and using back substitution , if needed.

Identify the row operation which transforms the matrix on the left to the matrix on the right.

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Compute the first three Jacobi iterations, using as the initial value for each variable. Then find the exact solution and compare.

The volume of traffic for a collection of intersections is shown. Find all possible values for , , , and .

Solve the given system using Gaussian elimination with three significant digits of accuracy. Then solve the system again, incorporating partial pivoting.

Use partial pivoting with Gaussian elimination to find the solutions to the system.

Find all solutions to the system

Determine which of the points (1, 0, -1, 0), (0, 1, 2, 3), and (2, 1, -1, -1) satisfy the linear system

Determine the value(s) of so that the following system is consistent.​

The volume of traffic for a collection of intersections is shown. Find the minimum volume of traffic from C to D.