a) List three statements that are equivalent to the statement: The matrix M is invertible. [5] b) The matrix 1 1 0 0 0 1 1 0 A= 0 0 1 1 4 11 9 2
has eigenvalues 5. 0. 0, 0. 0.
i) Determine the dimension of. and a basis for, the eigenspace of A associated
with the eigenvalue 0.
(ii) Without performing any further calculations, can you determine if the matrix A is similar to a diagonal matrix?
matrix A, but it has no entries equal to zero