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Unformatted text preview: R 4  x 1 + 2 x 3 = 0 and x 13 x 4 = 0 } c) The set of all 3 3 diagonal matrices in M (3 , 3). 4: Let V and W be vector spaces and let T : V W be a linear mapping with Null( T ) = { } . Suppose that { v 1 ,...,v k } a linearly independent set in V . Prove that { T ( v 1 ) ,...,T ( v k ) } is a linearly independent set in W . 1...
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