Mathematics 1229A/B Lecture Notes - Lecture 9: Fax, Asteroid Family

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: Mohsen Mollahajiaghaei

Document Summary

A linearequation in thevariables x acx t a2 2 t xn is one that can beputintheform t anxn b whereband a. Example an arc numbers thevariables are referredto as unknowns. 34 5 t 2 2 t 4 3 52 4 352. I x 2 t x z te x. 5 tax t 2 2 4 3 faxy t. 2 x y c 2 0 z 2x. Thislinearsystemis asystem oftwoequations in the3 unknowns x y z one solution is. 1 4 2 wehavemoresolutions for example 2 8 4 and. 0 o o we cancheckthatanypointintheformce 44 2 t solution where1 is an arbitrary real number so wehaveinfinitelymany solutions asolutionset ofthistype iscalleda one parameterfamilyof solutions here i is theparameter is a inconsistent consistent v c s v. Thissystemhas exactly 1solution if alinearsystemhas nosolution wesaythat it is inconsistent. Insolving a system of linearequations it isbettertobeginbyputtingthesystem intostandardformwhichmeanswriting it in such awaythat. 3 replace an equationwiththe sum of itselfand amultiple ofanother equation inthesystem.