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1d
comment Factoring $x^3-8$ by grouping
@Winther that works - but how did you figure that? Just made up?
1d
comment Factoring $x^3-8$ by grouping
Sorry, how did you realize that $x^3 - 8 = (x^3 + 2x^2 + 4x) + (-2x^2 - 4x - 8)$?
Jul
5
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?
Jul
5
comment Calculating an orthonormal base given another base.
By "second vector" you mean $(a,b,c)$?
Jul
3
comment Finding the smallest $x$ given a set of congruence conditions.
Did you mean $123$ instead of $133$?
Jun
22
comment How can a subspace have a lower dimension than its parent space?
Yes, that's exactly it! Thank you.
Jun
22
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.
Jun
17
comment Understanding the orthogonal complement of a subspace.
Ahhh it all makes sense. Yes, thank you.
Jun
17
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?
Jun
17
comment About an orthogonal complement theorem
@JulianP: You're right! I guess that's the problem?
Jun
16
comment Coordinate vector of a subspace of $\mathbb{M}_{2,2}(\mathbb{R})$
@user84413: I'm sorry, I didn't know that. I have added the basis. $\left\{ \left ( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}\right ) , \left ( \begin{matrix} 0 & 1 \\ 1 & 1 \end{matrix} \right )\right \}$
Jun
16
comment Coordinate vector of a subspace of $\mathbb{M}_{2,2}(\mathbb{R})$
@user156384: No. It may have been an error I guess. Just curious if perhaps there were multiple coordinate vectors (can there be?)
Jun
12
comment What to do with a hanging $1$ in a Karnaugh map?
@tpb261: Would it still be correct if I didn't group it with another $1$?
Jun
5
comment 'Obvious' theorems that are actually false
@MJD: If you keep expanding the surface area of the clay, won't it reach a point in which the distance between the atoms is great enough causing the clay to disintegrate? If that was the case, you shouldn't be able to expand a clay's surface area infinitely (I dunno, I'm no mathematician).
Jun
2
comment Creating groups with 10 men and 10 women.
Thank you, I think the formula in the first one confuses me. What is the logic behind it exactly? (Yeah I just used the same formula in the third question without knowing why)
Jun
2
comment Creating groups with 10 men and 10 women.
@DanielY: Well, yeah, no reason in particular. I just used the permutations formula. I think it's the same thing?
Jun
2
comment Creating digit sequences that can't begin with $0$, but one digit must repeat exactly once.
@RossMillikan: I see. So if the question meant that the two repeated digit must be together, I would apply Bananarama's answer?
Jun
2
comment Choosing two colours of different tones.
@user3678068: No, it doesn't count.
Jun
1
comment Counting when there are two inclusive conditions.
@vadim123: Ah, so the answer would be like $$2^7 + 2^4$$ I think?
Jun
1
comment Checking when a player has all four aces from a deck distribution.
@HennoBrandsma: Yeah, you're right. I fixed it now, thanks.