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Linear Algebra : Linear Maps and Kernel

Let L: V W be a linear map. Let w be an element of W. Let be an element of V such that L( ) = w. Show that any solution of the equation L(X) = w is a type , where u is an element of the kernel of D?

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Linear Maps and Kernels are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.