Let be an n times n matrix Which of the following is false I

Let be an n times n matrix. Which of the following is false? If is an eigenvalue, Ax = lambda x for some nonzero vector x. Row reducing A into echelon form is usually not an effective way of finding eigenvalues. If 0 is an eigenvalue of a matrix A, A is not invertible. If two eigenvectors are linearly independent, they correspond to distinct eigenvalues.

Solution

a) , c) ,d) are are correct and can be proved

b ) is False as It is known that if a matrix is given in upper triangular form, then we can just read off the eigenvalues (and their algebraic multiplicity) on the main diagonal of the matrix.

So, Option b is False