I was watching a youtube video on linear algebra and it gave the following equality. $\frac{1}{3}\left(\begin{matrix}1&2\\-1&1\\\end{matrix}\right)\left(\begin{matrix}4\\1\\\end{matrix}\right)=\left(\begin{matrix}2\\-1\\\end{matrix}\right)$ I must be mixing up my basics of matrix multiplication, ...

Is the set of all polynomials with a degree of at most six and with negative real numbers as coefficients a subspace of $\mathbb{P}_6$? I'm assuming this is asking if a polynomial of up to degree six covers all possibilities that can be produced. How do I determine the answer to this question? *E...

There is a tag called subspaces. (It seems that it was created by this user.) Both tag-wiki and tag-excerpt are currently empty, so the usage is unclear.1 If we consider just the name of the tag, there are plenty of situations where it can be used: vector spaces, topological spaces, metric spaces...

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 ...

For $a,b,c > 0$ prove: $$(a^2+b^2+c^2)(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}) +\frac{486(ab+bc+ca)^3}{(a+b+c)^6} \geqq 27$$ My work: I can easy found SOS for it: $$\text{LHS-RHS}=\sum {\frac { \left( a-b \right) ^{2}\cdot M}{{a}^{2}{b}^{2} \left( a+b+c \right) ^{6}}} \geqq 0$$ Where $M=\left(...