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     (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. (d) Find a basis for the column space of A. (e) Determine whether or not the rows of A are linearly independent.independentdependent    (f) Let the columns of A be denoted by a1, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.){a1, a2, a4}{a1, a2, a3}{a1, a3, a5}

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.

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

Find a basis for the row space and the rank of the matrix.−3 1 2 10 6 5−7 5 8(a) a basis for the row space

[Linear Algebra] 5. (a) Construct a matrix B whose null space consists of all linear combinations of vectors (2, 0, 7, 1) and (3, 1, −4, 0). (b) Express matrix B as a sum of two rank one matrices.