Give an example of a reduced row echelon matrix that describes a linear system having the stated properties. If it is not possible to find such an example, explain why not.
Write a reduced row echelon matrix for a linear system having five equations and three variables and having exactly one solution.
Write a reduced row echelon matrix for a linear system having three equations and three variables and having no solution.
Write a reduced row echelon matrix for a linear system having three equations and five variables and having infinitely many solutions.
Write a reduced row echelon matrix for a linear system having three equations and four variables and having exactly one solution.
Write a reduced row echelon matrix for a linear system having four equations and four variables and having exactly one solution.
Austin, Understanding Linear Algebra, §1.2 Finding solutions to linear systems, Exercise 3