Answer:
Following are the answers to this questions:
A) False.
B) False.
C) True.
D) True.
Step-by-step explanation:
In option A,
Let A is diagonal matrices that is,
here = 0, In this A is the nilpotent matrix and A has three values that are equal to 0 but it is not a diagonalizable matrix.
In option B,
If in given value A elements are 0 and 1 as a distinct eigen value, that's why A is diagonalizable but |A| =0 its means A is not invertible, that's why it is false.
In option C,
It is given that where A~ D, which is A is similar to diagonal matrices, that's why it is true.
In option D,
It is given that A has eigen vector, which leases from . A has eigen vector and A is matrix, the number of A eigen values = given vector of A, that's why it is correct.