Exam 2: Systems of Linear Equations and Matrices

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. ​ ​

Compute the product. ​

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

Let . Find . ​

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

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix. ​

The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.00/lb. If the blended coffee sells for $2.80/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.) ​ __________ lb of $3.00/lb coffee ​ __________ lb of $2.00/lb coffee

Solve the linear system of equations. If the system is inconsistent, indicate this. ​

Find the matrix A such that ​

Perform the indicated operations.

Given that the augmented matrix in row reduced form is equivalent to the augmented matrix of a system of linear equations, find the solution or solutions to the system, if they exist. ​ ​

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

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. ​ ​

Solve the system of linear equations, using the Gauss-Jordan elimination method. x₁ = __________ x₂ = __________ x₃ = __________

Find the inverse of the given matrix, if it exists. Verify your answer. ​ ​

Solve the linear system of equations ​ ​

(a) Find and show that . (b) Show that . (c) Show that .

Write the system of linear equations in matrix form. ​

Writing a matrix equation that is equivalent to the given system of linear equations solve the system using the inverse matrix. ​

Solve the linear system of equations. If the system is inconsistent, indicate this.