SOLVED: Find the basis and dimension for the row space, column space, and null space of matrices A and B.For both matrices A and B, show that the null space of each is orthogonal to the row space.Verify the rank-nullity theorem.Matrix A:[5 1 3 3][8 4 1 2][2 2 0 7][2 1 12 4][5 12 1 0 -2]Matrix B:[1 0 0][7 2 0][0 8 3][7 9 3][-3 9 0][0 0 0]

Find a basis for the column space of the matrix.8) B=⎣⎡​12−3​−... | Filo

Construct a matrix with the required property or say why that is impossible. (a) Column space contains [ 1 2 -3] and [ 2 -3 5], nullspace contains [ 1 1 1]. (b) Row space contains [ 1 2 -3] and [ 2 -3 5], nullspace contains [ 1 1 1]. (c) A x=[ 1 1 1] has a solution and A^T[ 1 0 0]=[ 0 0 0]. (d) Every row is orthogonal to every column ( A is not the zero matrix). (e) The columns ad