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]

SOLVED: 9. Construct a matrix with the required property, or explain why you can't. (1) The column space contains 6% and the row space contains [2] [H-]. (2) The column space has a basis of 2 and the nullspace has a basis of 3. (3) The dimension of the nullspace is 1 the dimension of the left nullspace. (4) The left nullspace contains 37 and the row space contains.

Column Space and Nullspace | Linear Algebra | Mathematics | MIT OpenCourseWare

Differential Equations and Linear Algebra, 5.1: The Column Space of a Matrix, A