Determine which of the following subsets of M 22 form subspaces. (a) The subset having diagonal elements nonzero. (b) The subset of matrices whose ( 1, 2) element is 0. (For example [ ] would be such a matrix.) ( c) The subset of matrices of the form [ a b ] . -b c (d) The subset of 2 X 2 matrices whose determinants are zero.

Week1:UnitCircle Sunday,August27,2017 3:50PM EquationtoFindEveryCoordinateontheUnitCircle: ! +% = 1 TerminalPoint ► Ifdistance(t)ispositivemarkoffthedistancealongtheunitcirclestartingat point(1,0)andmoveinacounterclockwisedirection.If(t)isnegativemovea distanceof|t|(absolutevalueoft)inaclockwisedirection.Anendpoint obtainedinthismanneriscalledtheterminalpoint. Question:Findthecoordinatesthatcorrespondtotheterminalp⎯⎯tt= * SolutionbyUsing:! + % = 1 ! = % Becausethispointcutstheunitcircleintwoequalpartsx=y ! +! = 1 xandyhavethesamevalue,xcansubstitutey 2! = 1 " 1