Find a basis for the subspace of P3 spanned by S = {13 +1 2 +2t + Lt3 -3/ + 1.12 + 1 +2

MATH​ ​103​ ​Chapter​ ​1​ ​Notes Problem​ ​Solving​ ​Techniques: ● Understand​ t​ he​ ​problem ○ Make​ ​sure​ ​that​ ​you​ ​read​ ​and​ ​analyze​ ​a​ ​problem​ ​carefully​ ​to​ ​completely understand​ ​what​ i​ t​ ​​ re​ ​trying​​ ind.f ● Devise​ ​ ​ ​plan ○ Since​ ​there​ ​are​ ​many​ ​different​ ​ways​ ​to​ ​solve​ ​a​ ​problem,​ ​decide​ ​which​ ​plan​ ​is​ ​the most​ ​appropriate​ ​for​ ​the​ ​particular​ ​problem​ ​you​ ​are​ ​solving. ● Carry​ ​out​ ​​ lanp ○ Make​ ​sure​ ​to​ ​fully​ ​carry​ ​out​ ​your​ ​plan​ ​once​ ​you​ ​decide​ ​on​ ​one.​ ​If​ ​it​ ​isn’t​ ​the​ ​best way​ ​to​ ​approach​ ​the​ ​problem​ ​and​ ​you​ ​run​ ​into​ ​a​ ​dead​ ​end,​ ​try​ ​something​ ​else! ● Look​ ​back​ ​an​ heck ○ Check​ ​over​ ​your​ ​answers​ ​to​ ​make​ ​sure​ ​they’re​ ​reasonable​ ​and​ ​thorough. Strategies​ ​for​ roblem​ ​ olving ● Use​ ​common​ ​sense ● Guess​ ​and​ ​check ● Use​ ​ rial​ ​​ rror ● Use​ ​inductive​ ​reasoning ○ drawing​ ​a​ ​general​ ​conclusion​ ​from​ ​repeated​ ​observations​ ​of​ ​specific​ ​examples ● Use​ ​deductive​ ​reasoning ○ applying​​ eneral​ ​principl​ o​ ​speci​ xamples ● Solve​ ​a​ ​similar,​ ​simpler​ ​problem ● Work​ ​backwards ● Write​ ​out​ ​a​ ​table ● Make​ ​a​ ​chart ● Find​ ​any​ ​patterns ● Make​ ​a​ ​sketch ● Use​ ​a​ ​formula​ i​ ​ pplies a ● Write​ ​an​ ​equation​ ​and​ ​solve​ ​it