The determinant is the product of the eigenvalues lambda 1 l

The determinant is the product of the eigenvalues lambda _1 lambda _2 .. lambda _n. Start with the polynomial det (A - lambda I) separated into its n factors. Then set lambda = 0. det (A - lambda I) = (lambda _1 - lambda) .. (lambda _n - lambda) so det (A) = (blank).

Solution

It\'s given in the first line that determinant of a matrix is given by the product of eigenvalues.

So,

lambda = L

det (A - LI) = (L1 - L)....(Ln - L)

when L = 0

det (A - 0*I) = (L1 - 0).....(Ln - 0)

det (A) = L1*L2*L3...... Ln

Substitute L = lambda