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More with Matrices and the Calculator Video Lecture Sections 11 1 and 11 2 Course Learning Objectives 1 Solve systems of linear equations using technology 2 Perform the algebra of matrices find inverses of matrices and solve matrix equations Weekly Learning Objectives 1 Solve systems of equations by elimination 2 Identify inconsistent systems of equations containing two variables 3 Express the solution of a system of dependent equations containing two variables 4 Solve systems of three equations containing three variables 5 Identify inconsistent systems of equations containing three variables 6 Express the solution of a system of dependent equations containing three variables 7 Perform row operations on a matrix 8 Solve a system of linear equations using matrices More Matrices and the Calculator An equation of the form EB FC G is called LINEAR since its graph is a line For a system of linear equations exactly one of the following is true 1 The system has exactly one solution Such a system is said to be 2 The system has no solutions Such a system is said to be 3 The system has infinitely many solutions Such a system is said to be This is easy to see geometrically if we have a system in two variables Although it is more difficult to visualize if we have a system of 8 equations with 8 variables the statement is still true In solving a system of equations we are attempting to find a solution by creating an equivalent system whose solutions are more obvious for us to see An equivalent system is a system whose solutions are the same as the original system If we use the elimination method then there are 3 operations that can be used to create an equivalent system 1 Add a nonzero multiple of one equation to another 2 Multiply an equation by a nonzero constant 3 Interchange the position of two equations page 1 Solve each of the systems 1 B B C C 2 B B C C 3 B B C C page 2 Note A system is said to be in triangular form if the second equation does not contain the first