I am looking through some old linear algebra exam papers. However i do not understand how to calculate whether a set of solutions is within a certain subspace R. This is the problem in question:
I think i understand how to check whether vectors are within a subspace R, but how would i calculate this?
Thanks a lot, really hope you can help me out!
$\endgroup$61 Answer
$\begingroup$The set of solutions of $A\mathbf{x}=\mathbf{b}$ is not a subespace of $\mathbb{R}^4$ becasuse the null vector $\mathbf{0}=\begin{bmatrix}{0}\\{0}\\{0}\\{0}\end{bmatrix}$ does not satisfy $A\mathbf{0}=\mathbf{b}$.
$\endgroup$6
