EE2007 Tutorial 7Linear AlgebraSystems of Linear EquationsExercise 1.[Gaussian Elimination Method](a) Solve the linear system using the elimination method.(b) Give restrictions ona,b, andcthat the linear system is consistent.(c) Consider the systemx1-x2+3x3-x4=1x2-x3+2x4=2(i) Described the solution set where the variablesx3andx4are free.(ii) Described the solution set where the variablesx2andx4are free.(d) Determine the values ofksuch that the linear systemKVL/Sep13
Exercise 2.[Elimination Method using Augmented Matrix]Write the linear system as an augmented matrix, and solve the linear systemExercise 3.The augmentation matrix of a linear system has the form-231a11-1b05-1c(a) Determine the values ofa,bandcfor which the linear system is consistent.(b) Determine the values ofa,bandcfor which the linear system is inconsistent.(c) When it is consistent, does the linear system have a unique solution or infinitelymany solutions?(d) Give a specific consistent linear system and find one particular solution.
EE2007 Tutorial 8Linear AlgebraRRE, Matrix Algebra, Inverse, Elementary MatricesExercise 4.[Matrix Operations]LetA=20-110-2,B=-311-311,C=3-1-1-3Whenever possible, perform the following operations. If a computation cannot be made,explain why.(a) 2A0-B0,(b)B0-2A,(c)AB0,(d)BA0,(e) (A0+B0)C,(f)C(A0+B0),(g) (A0C)B,(h) (A0B0)CExercise 5.[Reduced Row Echelon Form]Find the reduced row echelon form of the matrices-22-12033-31-422(b)4-3-4-2