engineering recuitment GATE CSE 2023-24 Test Series Engineering Mathematics Linear Algebra Matrix Algebra
Let M and N two n × n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively.
Which of the below-given statements is/are FALSE?
1
rank(M + N) ≤ rank(M) + rank(N)
2
rank(MN) = rank(M) rank(N)
3
det(MN) = det(M) det(N)
4
det(M + N) ≤ det(M) + det(N)