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

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

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.

Suppose that A and B are n×n matrices. Check the true statements below: A. If det(A) is zero, then two rows or two columns are the same, or a row or a column is zero.B. det(AT)=(−1)det(A)C. If two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix.D. The determinant of A is the product of the diagonal entries in A

Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)A = 2 0 0 0 1 00 0 3 B = 1 0 0 0 2 00 0 3

Find the inverse of the matrix 𝐴 = [2 3 44 3 11 2 4] by using elementary rowtransformations.