MAS 3105March 15, 2007Quiz 5 KeyProf. S. Hudson1) Find the matrix representationAof the linear operatorL:R2→R2that reflects eachvectorxabout the linex2=x1and then projects it onto thex1-axis.2) Answer TRUE or FALSE: Part a) refers to the ‘baby rabbit example’ from the lectures.a) With 2 adults and 3 baby rabbits this year, we’ll have 9 rabbits total, next year.b) The commuting diagram for Ch 4.3 (similarity) contains only one vector space,V.c) IfAis similar to itself, thenAis nonsingular.d) IfAandBare row equivalent they have the same column space.e) The matrixAthat answers problem 1) has rank = 1.3) Choose ONE of these.a) SupposeAandBare nxn andBis nonsingular.Prove that rank (BA) = rank(A). [Hint: compare their nullspaces]b) Suppose thatL:V→Wis linear andSis a subspace ofV. Prove thatL(S) is asubspace ofW.c) State the formula in Thm 5.1.1 forxTyand prove it (inR2).Remarks and Answers:The average was about 40/60.The unofficial scale is:A’s45-60, with 6 points per letter below that. I computed your semester average, based on
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