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 Oct25 comment Does the line $(2,1,1)+t(-3,1,5)$ live within the plane $31x+3y+18z=62$? @Galc127: The formula you posted, is that for calculating the orthogonal projection? In that case, don't I have to multiply the result by $(31,3,18)$, and then calculate the magnitude of the result? Oct24 comment Why isn't the orthogonal vector to a direction vector of a plane not necessarily perpendicular to such plane? Would the same apply parallel vectors? I mean, if I find a vector that is parallel to that line's direction vector, would it also be parallel to the plane? Oct1 comment Why $(-1 \cdot h) = -1$ when $h$ approaches $0$? By the way, if $h \not = 0$, how come the denominator is $(x-1)^2$? I had said that "$h$ is practically $0$" but I'm not that convinced anymore. Sep20 comment Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ @AndréNicolas I see now. Thanks. By the way, you picked $\frac{1}{4}$ because it made arithmetic easier - but how can I determine the "largest acceptable value" that can replace $\frac{1}{4}$? (out of curiosity) Sep20 comment Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ @EWHLee I see. I wonder if $\frac{1}{4x-9}$ should have been $\frac{1}{|4x-9|}$ instead... Wait, no, that doesn't work either. Goddammit. What should I have done instead? Sep20 comment Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ @AndréNicolas Ahhhh yes, that's right. By the way, isn't $|(x-3)| < \delta < \frac{9}{4}$ enough to keep $|4x-9|$ away from $0$ since $\frac{9}{4}$ is the solution to $4x-9$? Sep19 comment Proving $\lim_{x\to1}(x^2+3)=4$ Hm I'm not very sure how can $|x-1| < \delta$ lead to $|x+1|\le 3$. If you increase $|x-1|$ by $2$ to reach $|x+1|$, shouldn't it be $|x+1| \le 2$ rather than $3$? Sep19 comment Why does $|x-1|^2+3|x-1| < \epsilon \implies |x-1|^2 < \frac{\epsilon}{2} \ \ \land \ \ 3|x-1| < \frac{\epsilon}{2}$? @Oleg567: What if $a = b = \epsilon/2$? Sep7 comment For what values of $p$ and $b$ is the vector $(b,8,b+7)$ a solution of this system? Thanks, that's right (although $b$ yields $-5$). Sep7 comment For what values of $p$ and $b$ is the vector $(b,8,b+7)$ a solution of this system? @Adriano: Huh, it seems it should be $b = -5$. The exercise's answer seems to be wrong haha. Sep1 comment Is $A$ invertible if $ABAB^2 = I$? Only of the same size? Aug21 comment Factoring $x^3-8$ by grouping @Winther that works - but how did you figure that? Just made up? Aug21 comment Factoring $x^3-8$ by grouping Sorry, how did you realize that $x^3 - 8 = (x^3 + 2x^2 + 4x) + (-2x^2 - 4x - 8)$? Jul5 comment Calculating an orthonormal base given another base. Aha, this worked! I'll keep on testing it. Do you know why my particular approach didn't work? Jul5 comment Calculating an orthonormal base given another base. By "second vector" you mean $(a,b,c)$? Jul3 comment Finding the smallest $x$ given a set of congruence conditions. Did you mean $123$ instead of $133$? Jun22 comment How can a subspace have a lower dimension than its parent space? Yes, that's exactly it! Thank you. Jun22 comment How can a subspace have a lower dimension than its parent space? I'm sorry, I made a mistake with my example - the real core question is, how can a subspace have a lower dimension than its parent space? (according to the above theorem) - that's why I made up that example. Jun17 comment Understanding the orthogonal complement of a subspace. Ahhh it all makes sense. Yes, thank you. Jun17 comment Understanding the orthogonal complement of a subspace. And the orthogonal complement of a line in 3D is another line, too? Is a plane ever the orthogonal complement of something?