A:R^m->R^nKataKoniK said:Q: If A is an m x n matrix and rank A = m, show that m <= n.
I know that by definition if A is m x n, then rank A <= m and rank A <= n. However, I do not know how I would do this if rank A = m.
Any help would be great thanks.
I don't see what's troubling you. You know that:KataKoniK said:Q: If A is an m x n matrix and rank A = m, show that m <= n.
I know that by definition if A is m x n, then rank A <= m and rank A <= n. However, I do not know how I would do this if rank A = m.
Any help would be great thanks.
I think I see what you are saying, but I should make sure. For instance, if A is a 3x3 matrix with a 2-d null space, then you can uniquely choose the coordinate axes so that the null space plane satisfies the equation ax_2 + bx_3 = 0. Is this what you mean? If not, could you provide an example?mathwonk said:of course one should prove the reduced row echelon form is uniquely determined by the matrix. to see this one observes that the solution space of the matrix forms a subspace of R^n, and there is a unique way to choose a product decomposition of R^n so that that subspace is the graph of a function, with the indices of the domain space lexicographically as large as possible.