Answer true or false. Assume all matrices are square and all products ore define

Question

Answer true or false. Assume all matrices are square and all products ore defined. If Ax = lambda x for some vector x. then lambda is an eigenvalue of A. If u and v are linearly independent eigenvectors for some matrix A then they correspond to two distinct eigenvectors. A scalar lambda is an eigenvalue of A if and only if the equation (A - lambda I) x = 0 has a non-trivial solution. If Rn has a basis of eigenvectors of A then A is diagonalizable. lambda = 0 is an eigenvalue of A if and only if A is invertible.

Explanation / Answer

a)- false b)- true c)-false d)- true e)-false

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