Given that a matrix A3x3 has rank 2 and for the eigenvector

Given that a matrix A_3x3 has rank = 2 and for the eigenvectors

then

a) A is diagonalizable and invertible

b) A is not diagonalizable but is invertible

c) A is diagonalizable but not invertible

d) A is neither diagonalizable nor invertible

Solution

since rank of A = 2 and A is 3*3 matrix.so

rank (rank = 2) is not equal to n (n=3).

therefore it is not invertible.

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since number of eigen value is equal to n so this matrix is diagonalizable.