Write down orthonormal bases for the four fundamental subspaces [...]" 1. The problem statement, all variables and given/known data Problem: Write down orthonormal bases for the four fundamental subspaces of A = matrix([1,2],[3,6]]). (1 and 2 are on the first row whereas 3 and 6 are on the second row.) Solution: A = matrix([1,2],[3,6]]) is a 2 by 2 matrix of rank 1. Its row space has basis ##v_1##, its nullspace has basis ##v_2##, its column space has basis ##u_1##, its left null space has basis ##u_2##: Row space: 1/sqrt(5) matrix(,) Nullspace: 1/sqrt(5) matrix(,[-1]) Column space: 1/sqrt(10) matrix(,) Left nullspace: 1/sqrt(10) matrix(,[-1]) 2. Relevant equations Gram-Schmidt process (I think) 3. The attempt at a solution I watched videos on the Gram-Schmidt process but, they involve vectors whereas this involves a matrix, plus the concept with the vectors is still new to me so could someone help me with this super basic problem so that I can get started with the more complex ones please? Any input would be greatly appreciated!