Applications Of Determinants And Matrices

The parameter on which the value of the determinant does not depend upon, is

Let be a invertible matrix with real entries and let denote the identity matrix. If , then which of the following statements is/are ALWAYS TRUE?

Let α, β and γ be real numbers such that the system of linear equations



is consistent. Let represent the determinant of the matrix.

Let P be the plane containing all those for which the above system of linear equations is consistent, and D be the square of the distance of the point (0, 1, 0) from the plane P.