### Linear Transformations, Matrices, Projections, Reflections, Kernels, Vector Space, Rank and Nullity (11 Problems)

Please see the attached file for the fully formatted problems. 1 Prove that the solution space of AX = 0, where A is a m x n matrix, is a vector space. 2 Are the vectors x3 - 1, x2 - x and x linearly independent in P3 ? Why ? 3 Determine whether or not the function T : Mmn --> Mmn dened by T(A) = A + B, where B is a mix