(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let x [itex]\in[/itex] R^{N}, y [itex]\in[/itex] R^{M}& A [itex]\in[/itex] R^{MxN}be a matrix. Denote the columns of A by A_{k}, k = 1,...,N. Let R(A) & N(A) be the range & null space of A respectively.

a) How do the colmuns of A relate to the range of A?

b) Your task is to find the solution to the problem y = Ax, where y & A are known & M = N. What role do R(A) & N(A) play?

c) Let R^{N}[itex]\ni[/itex] x = (x_{1},x_{2}), x_{1}[itex]\in[/itex] R^{N1}, x_{2}[itex]\in[/itex] R^{N2}& N_{1}+ N_{2}= N. Let A [itex]\in[/itex] R^{N1xN}& consider the problem Ax = 0. Assume that you know x_{2}. Solve for x

2. Relevant equations

3. The attempt at a solution

a) This is easy, the column space of A is just the range of A.

b) Do we just use the definitions of R(A) and N(A)?

c) I have no idea on this one.

Any help please.

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# Homework Help: Range & Null space of A matrix

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