tut2 - T : R 2 → M (2 , 2) deﬁned by T ( a, b ) = ± a...

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Math 235 Tutorial 2 Problems 1: Let B = { 7 x + 5 , - 3 x - 1 } and C = { x - 5 , - 2 x + 2 } be bases for P 1 . Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B . 2: Determine the matrix of the linear operator L : R 2 R 2 with respect to the basis B and determine [ L ( ~x )] B where B = { ~v 1 ,~v 2 } , L ( ~v 1 ) = ~v 1 + 3 ~v 2 , L ( ~v 2 ) = 5 ~v 1 - 7 ~v 2 and [ ~x ] B = ± 4 - 2 ² . 3: Find the matrix of each linear operator with respect to the given bases B and C . a) L : P 2 R 2 deﬁned by L ( ax 2 + bx + c ) = ( a + c, b - a ), B = { x 2 +1 , x +1 , x 2 + x - 1 } , C = { (1 , 0) , (1 , 1) } . b)
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Unformatted text preview: T : R 2 → M (2 , 2) deﬁned by T ( a, b ) = ± a + b a-b ² , B = ³± 2-1 ² , ± 1 2 ²´ , C = ³± 1 1 0 0 ² , ± 1 0 0 1 ² , ± 1 1 0 1 ² , ± 0 0 1 0 ²´ . 4: Let B = ³± 2 3 ² , ± 1 2 ²´ and C = ³± 2 1 ² , ± 1 1 ²´ and let L : R 2 → R 2 be the linear mapping such that [ ~x ] B = [ L ( ~x )] C . Find L µ± 1 1 ²¶ . 1...
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This note was uploaded on 01/27/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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