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squenshl
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Homework Statement
Let x [itex]\in[/itex] RN, y [itex]\in[/itex] RM & A [itex]\in[/itex] RMxN be a matrix. Denote the columns of A by Ak, 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 RN [itex]\ni[/itex] x = (x1,x2), x1 [itex]\in[/itex] RN1, x2 [itex]\in[/itex] RN2 & N1 + N2 = N. Let A [itex]\in[/itex] RN1xN & consider the problem Ax = 0. Assume that you know x2. Solve for x
Homework Equations
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.