Linear Equations PDF

ly emsof lineareqatins a X ax anXn b thing Epe 1.4177 2 x linear rearrange 3x 5 3 2 3 1 0 2 5 2 YEG Expl Is 4x 5 2...

ly emsof lineareqatins a X ax anXn b thing Epe 1.4177 2 x linear rearrange 3x 5 3 2 3 1 0 2 5 2 YEG Expl Is 4x 5 2 x x linear No b c of x x2 term A zXz An Xn b An X Az X 922 2 Aan Xn bz And am xn m AmiX Xzt Tatnf_ is m equations in n unknowns  A solution to is an ordered n tuple in X1 X2 Xn that makes all equations true The solutionset of A is the set of all solutions Thm Thereareonly3possibiliti.es 11 my mom ÉÉffÉÉ É if f rEhu and n columns of numbers with m rows The coefficientmatic of is men mean aim The augmentedmatic of 1 1 is mxent ami aim m me EITEY.cn fntf cR Ri 2 Interchange Ri R CR Ri 0 3 Scaling systTugmented matrix ffff.fm new new augmented system matrix TheThenewsystemhasthesamesolutiont set as the original system  ÉI he solution set of the system no Ox 2 2 8 3 8 5 0 2 5 3 10 Augmented matrix C R.se 1 1 RER i Tugmeted matrix  same solution set new system x as original y IT Onesolutioni1110 reversible row operations are Elementary R Ri cRi Ri reversed by Ri R Ri R Ri 1 Ri CR Ri Rita Rj Two matrices A and B are rowhivalent if A can be transformed into B using elementary row operations have augmented matrices If two linear systems that are equivalent row then they have the same solution set rewording of earlier thm Expl 3 The following system consistent X2 4 3 8 2x 3 2 2 3 1 msistat.is I i meon augmented matrix rent Es new augmented matrix 2 3 2 3 1 set same soln 1 2 new system 2 4 original as new system has no solutions original system is inconsistent