An n×n matrix A is diagonalizable if A is invertible.A. TrueB. False
Question
An n×n matrix A is diagonalizable if A is invertible.A. TrueB. False
Solution 1
To determine if an n×n matrix A is diagonalizable, we need to check if A is invertible.
Step 1: Check if A is invertible. If A is invertible, then it is diagonalizable. If A is not invertible, then it is not diagonalizable.
So, the statement "An n×n matrix A is diagonalizable if A is invertible" is true.
Therefore, the answer is A. True.
Solution 2
To determine if an n×n matrix A is diagonalizable, we need to check if A is invertible.
Step 1: Check if A is invertible. If A is invertible, then it is diagonalizable. If A is not invertible, then it is not diagonalizable.
So, the statement "An n×n matrix A is diagonalizable if A is invertible" is true.
Therefore, the answer is A. True.
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