Test: Matrices & Determinants - 1 - Mathematics MCQ

If the eigen values of a square matrix be 1, - 2 and 3, then the eigen values of the matrix 3A are

If the two eigen values of are 3 and 15, what is the third eigen value?

The eigen values of matrix A = are

Let Then

The rank of matrix is

If A is 3 × 4 matrix and B is a matrix such that A'B and BA' are both defined, then the order of B is

If ω is the cube root of – 1, then the value of is

Let identity inλ, where p, q, r and s are constants, then value of t is

If a = b = c = 0, then the determinant  is divisible by

If a² + b² + c² = 0 then value of is

The value of is

Value of determinant is

The value of is

Study the following assertions about a square matrix
(i) The sum of the eigen values of A is equal to its trace
(ii) The product of the eigen values of A is equal to its determinant
(iii) All eigen values of A are non-zero, if and only if A is non-singular
(iv) If A^-1 exists, then the eigen-values of A^-1 are equal to the reciprocal of the eigen

Q. Which of the following is correct with respect to above assertions?

The value of the determinant is

If ω is an imaginary cube root of unity, then the value of is