Question

equat o find systems of 3 - Vertable sons such that cel The set of solutions is a line 2) The set of solutions is a faint c) The set of solutsuns is empty Like there is no solution).

Answer 1

Tell the System of equations of three variables be A X =B bi N Where AD X= (3 ) Bo/62 all a2 a3 A22 A23 Az a33 Aal bz azi A a of and matrina the rank of has than Coefficient matring, and augmented matrix [A:B] have the same is equal to a then than nostoon to set of solutions is a line. 6 of coefficient js 3 system unique ae solution a point, If me rance of coefficient ma augmented materia CA ?B? are unequal then the set of solution is empty it is mabin and 1 all I liustration of point, (a): If Rank A = Rank (A: 0] is less than 2 ie Rome A = Rance (A:0] = 1 hew Ihe three planes are identical, ie mey meel and a plane. But to get a line of as Solutions Rank A = Ram (A:B] =2. le any of tro equat nation meet a line. then