
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^...

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...

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.
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

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 ...
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