Homework SourseFind k such that Nul A is a subspace of Rk and find l such t
Find k such that Nul (A) is a subspace of R^k, and find l such that CoI (A) is a subspace of R^l, where A = [7 - 2 0 - 2 0 - 5 0 -5 7 - 5 7 - 2]![Find k such that Nul (A) is a subspace of R^k, and find l such that CoI (A) is a subspace of R^l, where A = [7 - 2 0 - 2 0 - 5 0 -5 7 - 5 7 - 2]SolutionA is a](/WebImages/43/find-k-such-that-nul-a-is-a-subspace-of-rk-and-find-l-such-t-1133248-1761605918-0.webp "Find k such that Nul (A) is a subspace of R^k, and find l such that CoI (A) is a subspace of R^l, where A = [7 - 2 0 - 2 0 - 5 0 -5 7 - 5 7 - 2]SolutionA is a")
Solution
A is a 4x3 matrix. Further, Null (A) is the set of solutions to the equation AX = 0. Then X has to be a 3-vector. Hence, if Null(A) is a subspace of Rk, then k = 3. Also, Col(A) will have 4-vectors. Hence, if Col(A) is a subspace of Rl, then l = 4.
