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quiz3

# quiz3 - Name Linear Algebra Quiz 3 1 2 1 3 2 and = cfw 1 1...

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Name: Linear Algebra Quiz 3 June 13, 2006 1. Consider R 2 with ordered bases β = { 2 1 , 1 1 } and γ = { 3 1 , 2 1 } . (a)(4 points) Find the transition matrices from β -coordinates to standard coordinates, γ - coordinates to standard coordinates, and γ -coordinates to β -coordinates, i.e., find [id] STD β , [id] STD γ , and [id] γ β . (b) (4 points) Let L : R 2 R 2 by L x y = 2 x + y - x + 3 y . Show that L is a linear transfor- mation and find a matrix A such that L ( x ) = Ax for all x R 2 . (c) (4 points) Find the matrix representing L with respect to the bases β to β and β to γ , i.e., find [ L ] β β and [ L ] γ β . (d) (4 points) Suppose x = 2 3 1 - 2 1 . Find the coordinate representation of x with respect to the ordered bases β , γ , and the standard basis, i.e., find [ x ] β , [ x ] γ , and [ x ] STD . (e) (4 points) Find the coordinate representation of L ( x ) with respect to the ordered bases β , γ , and the standard basis, i.e., find [ L ( x )] β , [ L ( x )] γ , and [ L ( x )] STD . Solution:
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