Find the value of b such that the rank of the matrix A is 3.A =[1 1 −1 04 4 −3 1𝑏 2 2 29 9 𝑏 3

Matrix A and B are given below:A =1 −3 4 −1 9−2 6 −6 −1 −10−3 9 −6 −6 −33 −9 4 9 0 and B =1 −3 0 5 −70 0 2 −3 80 0 0 0 50 0 0 0 0Assume that the matrix A is row equivalent to B. Find(a) (3 pts) rank A.

. Find the rank of the matrix A by normal form method where1 2 1 34 1 2 1 .3 1 1 21 2 0 1

Use the fact that matrices A and B are row-equivalent.A = −2 −5 8 0 −17 1 3 −5 1 5−5 −9 13 7 −671 7 −13 5 −3B = 1 0 1 0 1 0 1 −2 0 30 0 0 1 −50 0 0 0 0(a) Find the rank and nullity of A.rank nullity

Are there two 3 by 3 matrices A and B, both of rank 2,such that AB is the zero matrix? Explain your answer.1

If A and B are 3 × 3 real matrices such that rank(AB) = 1, then rank(BA) cannot be