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I have read everywhere that the resolution of the linear system $$Ax+b=0$$ where $A\in S_n(\mathbb R)$ and $b\in \mathbb R^n$ is equivalent to the resolution of the following optimization problem: $$f(x)=\frac 12\langle Ax,x\rangle+\langle b,x\rangle.$$ Which means that if $x\in \mathbb R^... 0 I need help making progress on a linear algebra question. Consider the subset$W = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ \end{bmatrix}$such that$x_1 + x_2 + x_3 = 2$Does$x = \begin{bmatrix} 1 \\ 0\\ 1\\ \end{bmatrix} \in W?$Does$u = \begin{bmatrix} 1\\ 1\\ 1\\ \end{bmat...

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Show that if $V$ is a nonzero vector space over $\mathbb{R}$, and $V_{1}, V_{2},\ldots V_{k}$ are proper subspaces of $V$ then there exists $v\in V$ such that $v\not\in V_{i}$ for any $1\leq i\leq k$ I can prove the case for $k=2$ but I cannot produce an induction argument.

The tag has been removed before:

### Removal of (subspaces) tag

Dec 2 '16 at 13:45, 1 day total – 40 messages, 4 users, 0 stars

Bookmarked Dec 3 '16 at 14:15 by Martin Sleziak

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Update. The subspaces tag has been removed thanks to a friendly neighbourhood Community Manager. There's another possibility that hasn't been mentioned in the OP, and the one I would prefer: kill it! I don't see subspaces as a tag that will ever be consistently used, and not something that ...

@learnmore I will point out that subspaces tag has been discussed on meta previously and it has been removed (even blacklisting was discussed): See meta.math.stackexchange.com/questions/21345/… and chat.stackexchange.com/rooms/20352/conversation/…Martin Sleziak 10 secs ago
I removed from both questions linked above.