quizzes-Lina.2011t - Lina MAS4105 Q5 Frid Let R be the std...

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Lina MAS4105 Quizzes Q 29Sep2010 Q1: Tues. 6 Sep Matrix-product h 2 3 4 5 i · h 7 w 2 1 i = . . . . . . . . . . . . . Matrix-add distributes over matrix-mult: T F Q2: Wedn. 7 Sep In R -VS V , collection E = { u 1 , . . . , u 7 } is linearly-indep if . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In VS V , collection B V is a basis if . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [Imagine 3 blank lines] Q3: Frid. 16 Sep May lightning strike this table! ( I.e, please fill in. ) n r n q n s n t n 0 131 1 0 1 56 0 1 2 3 4 5 Thus 1 = [ . . . . . . · 131] + [ . . . . . . · 56]. So the soln to congruence 56 x 131 8 is x = . . . . . . . . . . . . . . . . [ 0 .. 131 ) . Q4: Wedn. 21 Sep i The map Ply 3 Ply 3 which sends f 7→ g , where g ( x ) := x · f 0 ( x + 5), is: Circle best LinearAffineNeither ii Suppose T is a linear map from R 3 to R 2 . Let { e 1 , e 2 , e 3 } be the standard basis for R 3 , and let { v 1 , v 2 } be the standard basis for R 2 . Suppose that T ( e 1 ) = 17 v 1 - 2 v 2 and T ( e 2 ) = 6 v 2 and T ( e 3 ) = 4 v 1 - 3 v 2 . Then the matrix of T is: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q5: Frid. 30 Sep Let R θ be the std. rotation [ by θ ] matrix. With U := 1 2 · 3 1 1 3 and M := 1 1 1 1 , the product [ UM ] 45 = α · R θ , with α = . . . . . . . . . . . . .
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