Determinants Lecture 2

Antigenic determinants are

A determinant is chosen at random from the set of all determinant of order 2 with elements 0 or 1 only. Find the probability that the determinant chosen is nonzero.

Using properties of determinants, prove that 3 2 (a 1) 3 3 1 2a 1 a 2 1 a 2a 2a

Find the number of nonzero determinant of order 2 with elements 0 or 1 only.

Using properties of determinants, prove the following: |[1,a,a^2],[a^2,1,a],[a,a^2,1]|=(1-a^3)^2

Which of the following is correct (A) Determinant is a square matrix. (B) Determinant is a number associated to a matrix. (C) Determinant is a number associated to a square matrix. (D) None of these

Entries of a 2 xx 2 determinant are chosen from the set {-1, 1} . The probability that determinant has zero value is

If D is determinant of order three of Delta is a determinant formed by the cofactors of determinant D: then

If A=[1 3 2 1] , find the determinant of the matrix A^2-2A .

If A=[1 3 2 1] , find the determinant of the matrix A^2-2Adot