Consider a linear homogeneous system of equations Ax = 0, where A is an 𝑛 × 𝑛 matrix, x is an 𝑛 × 1 vector and 0 is an 𝑛 × 1 null vector. Let 𝑟 be the rank of...

If a matrix 𝑀 is defined as the sum of all the eigenvalues of 𝑀3 is equal to __________ (in integer).

A system of n homogeneous linear equations containing n unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is