Question: Prove that if A is diagonalizable then trace(A) is equal to the sum of all its eigenvalues. For triangular matrices this problem is pretty obvious,

Prove that if A is diagonalizable then trace(A) is equal to the sum of all its eigenvalues.

For triangular matrices this problem is pretty obvious, however I don't know what to do for regular nxn matrices

Prove that if b is in Col(A), then Ax=b is a consistent system

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