Suppose that V is a 5-dimensional vector space. Let L: V rightarrow V be a linea

Question

Suppose that V is a 5-dimensional vector space. Let L: V rightarrow V be a linear transformation. Decide whether each of the following statements is true or false. If you do not have enough information to decide whether a statement is true or false, select "Impossible to tell". If u1 , ..., u5 is any basis of V, then it is possible to write a matrix for L in terms of this basis. If L has eigenvectors v1,...,v5 which are linearly independent, then L is diagonalizable. Fix some nonzero vector v. If every eigenvector of L is a constant multiple of V, then L is diagonalizable. If there is some basis w1, ..., w5 with respect to which the matrix of L is a diagonal matrix, then w1,... ,w5 are eigenvectors of L.

Explanation / Answer

1)True 2)False 3)True 4)Impossible to tell

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