tut5 - L ? b) Is (2 , 1 , 3 , 0) in the range of L ? c) Is...

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Math 136 Tutorial 5 Problems 1: a) Let S : R 2 R 2 be a stretch by a factor of 5 in the x 2 -direction. What is the standard matrix of S . b) Calculate the standard matrix of the composition of S followed by a rotation through angle π 3 . c) Calculate the standard matrix of the composition of S following a rotation through angle π 3 . 2: Prove that if ±x M (2 , 3) and a, b R , then a ( b±x ) = ( ab ) ±x . 3: Let L be the linear mapping with matrix [ L ]= 12 - 1 25 - 3 14 - 3 1 2 0 . a) What is the domain and codomain of
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Unformatted text preview: L ? b) Is (2 , 1 , 3 , 0) in the range of L ? c) Is (2 , 4 , 2 , 1) in the range of L ? If so, Fnd v such that L ( v ) = (2 , 4 , 2 , 1). d) Determine a spanning set for the range of L . e) Determine a spanning set for the nullspace of L . 4: Determine the matrix of a linear mapping L : R 2 R 2 whose nullspace is span { (1 , 2) } and whose range is span { (1 , 2) } . 1...
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