Question) Consider the following matrix. A = 1 0 0 1 0 0 (1) Find rank(A), a basis for the column space of A, C(A), a basis for the row space of A, C(AT ), a basis for the null space of A, N(A), and a basis for the left null space of A, N(AT ). Hint: For a m n matrix A, the column space of A is defined as C(A) = {Ax|x Rn} Rm, and the row space of A is defined as C(AT ) = {AT y|y Rm} Rn. Also, the nullspace N(A) is defined as {x Rn|Ax = 0} Rn. For the same matrix, the left nullspace N(AT ) is defined as {y Rm|AT y = 0} Rm. Also, we have dim(C(A)) + dim(N(AT )) = m dim(C(AT )) + dim(N(A)) = n. [Note: You need to use Gaussian elimination to answer this question. For all the linear systems in this assignment, you need to use Gaussian elimination to solve them.]