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tut1 - x a 22 c L M(2 3 → M(2 3 where L ±² a b c d e f...

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Math 235 Tutorial 1 Problems 1: Find a basis for the row space, column space and nullspace of A = 1 6 0 2 - 1 0 0 1 - 2 1 0 0 0 0 1 0 0 0 0 0 . 2: Find a basis for the range and nullspace of the following linear mappings and verify the Rank-Nullity theorem. a) proj (1 , - 2 , 2) : R 3 R 3 . b) L : M (2 , 2) P 2 , where L a 11 a 12 a 21 a 22 = a 11 x 2 + ( a 12 + a 21 ) x + a 22 . c) L :
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Unformatted text preview: x + a 22 . c) L : M (2 , 3) → M (2 , 3) where L ±² a b c d e f ³´ = ² d e f 0 0 0 ³ . 3: Let V and W be n-dimensional vectors spaces over R and let L : V → W be a linear mapping. Prove that Null( L ) = { ~ } if and only if the range of L is W . 1...
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