Question

In matrix algebra, which option is not correct about an eigenvalue problem of the type Ax = Lx?

(a) It has a discrete solution

(b) It has solution only if A non-singular

(c) x is called eigenvector

(d) L is called eigenvalue

This question was posed to me in my homework.

Question is from Eigen Value and Time Dependent Problems in division Single Variable Problems of Finite Element Method

Answer 1

Correct choice is (b) It has solution only if A non-singular

Explanation: An eigenvalue problem of the type Ax = Lx looks as if it should have a continuous solution, but instead, it has discrete ones. The problem is to find the numbers denoted by L, called eigenvalues, and their matching vectors denoted by x, called eigenvectors. It may have a solution irrespective of whether the matrix A is singular or not.