There are different properties of determinants that enables us to calculate determinants easily. For example, one of the property is that if all the elements of any row or column of matrix are equal to zero then determinant of such a matrix is equal to zero. Another
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For example, we are given any n x n matrix A and we want to calculate its Eigen values and eigen vectors. Then, we must have non-zero vector x such that Ax=λx, where λ is an Eigen value and x is eigen vector. When we solve this equation, we get values of λ and x.
Tridiagonal matrices are the matrices which are having non-zero elements on the diagonal, super diagonal and subdiagonal. All the rest of the elements are zeros.