Let n > 1. Consider an n x n matrix M with elements from R. Let the vector (0, 1, 0, 0, ..., 0) in R^n be in the null space of M. Which of the following options is/are always correct?(A) Determinant of M is 1.(B) Determinant of M is 0.(C) Rank of M is 1.(D) There are at least two non-zero vectors in the null space of M.

For n > 1, the maximum multiplicity of any eigenvalue of an n x n matrix with elements from R is:

The determinant of a 4 x 4 matrix A is 3. The value of the determinant of 2A is ____________. (answe…

Consider the system of linear equations given below:ax + y = b16x + ay = 24Suppose the values of a a…

Let L, M, and N be non-singular matrices of order 3 satisfying L² = L⁻¹, M = L⁸ and N = L². Which ON…

Let A be an n x n matrix over the set of all real numbers R. Let B be a matrix obtained from A by sw…

Let A = [[1,2,3,4],[4,1,2,3],[3,4,1,2],[2,3,4,1]] and B = [[3,4,1,2],[4,1,2,3],[1,2,3,4],[2,3,4,1]].…