Question: Prove the statement in the photo. Problem 4 Prove the following statement: For any positive integer n and any n X 11 matrix A, if

Prove the statement in the photo.

Problem 4 Prove the following statement: For any positive integer n and any n X 11 matrix A, if A has distinct real eigenvalues A1, . . . ,Ap, then there exists a pdimensional subspace H of IR\" such that H is invariant under the transformation 53 I> A55

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