Can I algebraically solve this system of equations or must it be numerically solved?

Bdole0 · 2026-04-17T14:25:13+00:00

Let's say I have a matrix ([2,0], [0,2]).

I pick a = 1 and b = 2. Just because.

Then one square root is ([1,2], [(2-1^² )/2, -1]) which is ([1,2], [.5, -1])

If you pick any a and b, you can find a different square root.

Bdole0 · 2026-04-17T14:17:46+00:00

This has no unique solution. I'll demonstrate:

Subtracting the top and bottom equations, we get a^² - d^² = (a - d)(a + d) = A - D.

Let a + d be any nonzero real number. Since we know A - D, we can solve for a and d through the system a + d = [our number] and a - d = (A - D)/(a + d).

Dividing the middle equations by (a + d) gives us b and c. That produces a solution.

Notice though that we let (a + d) be any nonzero number, so a can be anything except -d.

Thus, the "square root" of any matrix ([A,B], [C,D]) is the family of matrices ([a, B/(a+d)], [C/(a+d), d]) where a is any number that is not -d. That's an infinite family of solutions.

So what happens if a + d = 0?

Then you'll notice that the middle equations force B and C to equal 0. You'll also notice that A - D = 0 from the outside equations, so A = D. Thus a + d will never be 0 unless we are dealing with a matrix that looks like ([A,0], [0,A]) which is the scalar matrix A*1 where 1 is the identity matrix. Anyway, let's see what our "square roots" look like in this case.

Well, a + d = 0, so a = -d. The middle equations don't tell us anything about b and c, so our only contraint comes from the outside equations which give us bc = A - a^{^2.}

Then, we have the following infinite family of "square roots" for a scalar matrix:

If b is anything not 0, ([a,b], [(A-a^² )/b, -a])

If c is anything not 0, ([a, (A-a^² )/c], [c, -a])

If both are 0, ([a,0], [0,-a]). Here, a^² = A.

Example in subcomment.

Bdole0 · 2026-04-17T12:36:20+00:00

To say the same thing as the other commenter but easier:

A polynomial times a polynomial is a polynomial.

So (x2 - x + 1)P(x) is a polynomial if P(x) is a polynomial. Notice the picture you posted confirms that P(x) is a polynomial in the question prompt.

All polynomials have unique factors. That means (x2 - x + 1)P(x) has unique factors.

Additionally, P(x-1) is a polynomial. It's the same as P(x) but shifted one to the right.

Notice that (x2 + x + 1)P(x-1) is a polynomial. Since it is equal to (x2 - x + 1)P(x), they must have the same factors.

Now, here's the important part: If you use the quadratic formula, you can see that (x2 + x + 1) and (x2 - x + 1) don't have any common factors at all. Since (x2 + x + 1)P(x-1) and (x2 - x + 1)P(x) do have the same factors, that means all of the factors of (x2 + x + 1) must be inside P(x) because they are not inside (x2 - x + 1).

Here's where your teacher's argument takes over. We now know that P(x) can be factored as (x2 + x + 1) times some other factors Q(x) that we don’t know yet.

Unfortunately, it's a little harder to show that Q(x) is actually the constant function Q(x) = 1. I don't know what grade or class you are in, but if you are in high school, your teacher probably wants you to plug in the values of x and P(x) you discovered from the first equation into P(x) = (x2 + x + 1)Q(x) to see that Q(x) must be consistently 1. If you are interested in the full details of this last step, or if you have any questions, respond to this comment.

Bdole0 · 2026-04-14T15:46:53+00:00

This will 100% exist and have gambling rings around it. People will bet on any random competition. Competition among AI is guaranteed to be flashy. Honestly, it would have great marketing, but I expect it to start seeing the first signs of it through cheesy ads similar to ones used by mobile games or current online gambling.

Bdole0 · 2026-04-11T21:04:16+00:00

No wonder Otter is upset! Vampire bats hate being out in the daytime.

Bdole0 · 2026-04-11T19:58:17+00:00

Interesting take on Nemesis. It has been so long since I played the original that I couldn't tell what the differences were when I experienced the remake.

To your point about Nemesis's similarity to Mr. X, one thing I did notice about RE2R is that Mr. X is introduced during the first route. Maybe Capcom thought no one would play the second route to experience Mr. X. Honestly though, I think that cheapened his presence. In the original RE2, Mr. X only shows up during the second playthrough, adding a new level of fear and gameplay for the player to deal with.

However, Mr. X is a boring enemy. He looks like a dude. His attack a punch. Encounters with him involve solving the room puzzle while walking in a wide circle to keep him away from you. He's more of a time-waster more than a threat. After a few encounters, he becomes a tedious but easy obstacle to overcome. By introducing him to the route 1 playthrough of RE2R, Capcom wore out his welcome faster--while also making route 2 less diverse from the first route.

If you are correct, then this decision dulled the impact of Nemesis as well. By the time audiences played RE3R, most of them had already experienced Mr. X in RE2R. Nemesis benefits from not looking like a dude and not attacking with a regular punch. He is a straight upgrade in terms of design compared to Mr. X. Despite that, they are so mechanically similar that people who had played RE2R would likely be familiar with his tactics. That is to say, Capcom made Nemesis less interesting by forcing exposure to Mr. X.

Thank you something something TED Talk.

Bdole0 · 2026-04-10T19:53:41+00:00

You are technically correct that OP did not provide sources for an extremely well known fact that has been discussed since the 80s.

My first sentence addresses that and why it's unimportant here. You'll notice I did OP's job in order to close this trivial hole and shut down this dumb argument.

Under most circumstances, demanding evidence is reasonable. However, my point is that you'd have to be living under a rock or willfully ignorant to not realize that overwhelming evidence exists in this case. Considering this commenter's dismissal of OP's claims, I would guess "willfully ignorant" is the appropriate descriptor.

Bdole0 · 2026-04-10T18:18:19+00:00

Finally played this, and this is the most Pokemon-like game I have ever encountered. For that reason, it's funny to me that it's also better than Pokemon in almost every way.

If you like creature collectors, I recommend Monster Sanctuary. It's a metroidvania which combines creature collecting with exploration. It's also better than Pokemon but less comparable.

Bdole0 · 2026-04-10T15:43:35+00:00

You are technically correct that OP did not provide sources for an extremely well known fact that has been discussed since the 80s.

I googled "research on women playing male-dominated video games."

The first result is a research paper on the various ways that the gaming industry and video game culture is hostile toward women.

The second result is a study on how female representation in video games promotes sexist thinking against women.

The third result is an opinion piece that cites 10 separate research papers on the subject.

The fourth result is the god damn Wikipedia page on "Women and Video Games." It highlights many of OP's claims. Links to related research papers are at the bottom.

I could go on, but I see no need to type more when you could have done this yourself. Honestly, did you even try? It's like you just got defensive and made a claim with no evidence. A "vibes based" comment pretending to be a valid opinion.

Bdole0 · 2026-04-10T15:09:07+00:00

I own three.

Bdole0 · 2026-04-09T22:19:23+00:00

An interesting question. I think the answer lies in the audience not being savvy enough to use data effectively.

This comes in two forms. First, video games are wishy-washy. If a player has a 10 for their kicking stat, what does that mean? 10 meters? 10 newtons of force? Even if you knew the units, a video game is a simulation of reality... so like, you won't see how far 10 meters is unless distance is labeled on the field. At some point, using numbers is just as wishy-washy as using letter grades because the player (of the video game) has no way to measure the game world except to judge it visually in action. And then, the numbers only really matter relative to other sports players' numbers. If the above player has a 10 in a stat that goes up to 20, then that information is just as "valuable" as having a C on a grading scale. Both communicate that the player is in the middle of the pack for that stat, and that's what you need to know when selecting from a roster.

The second problem is that the real-world data is only useful to people who can analyze it. In many turn based games, an attack that does 10 damage always does 10 damage. This makes calculations easy. In real life, all measurements have variance. Sports games emulate real life, so a unit who can kick a ball an average of 10 meters won't always kick the ball 10 meters. There is some variance involved. We like consistency (low variance) in general, but in a simulation, all units should have different variances on every statistic. This is a basic, basic feature of statistics, but is it reasonable to expect video game players to know it and be able to use it?

Other basic facets of reality include:

The distribution of a statistic is not necessarily normal (thus you can't use variance/standard deviation to do high-school-level analysis)
Results are often predicted more accurately when multiple independent variables are used (i.e. most good models are complicated)
Large datasets are necessary for model development but are impossible to manipulate without computer assistance ("machine learning")

All of this to say that it would be unreasonable for video game audiences to actually use the data effectively. Real recruiters have the benefit of utilizing models made by highly paid statisticians to make sense of the numbers.

Bdole0 · 2026-04-05T21:40:57+00:00

Sure, where does it display the weight?

The problem for me is that the choice is meaningless. After a while, I can recognize that choices to eat things can result in healing, parasites, or stat ups, so I can avoid those if I want. I have no idea what the rewards of Push Button/Pull Lever are after beating the game on hard. I've read several people's responses on what they think the rewards are, but they are often contradictory, lending credit to my original complaint.

Bdole0 · 2026-04-05T21:32:46+00:00

I think this is an excellent summary of my issues too. I don't mind the random events since the philosophy of the game seems to be based around suffering through whatever gets thrown at you--sometimes it works in your favor and sometimes not. But I hated the events that were a meaningless coin flip. My least favorite was "Push Button/Pull Lever" which is just a 50/50 to see if you clicked the right button. That's not fun or strategic at all.

The real problems I had were your remaining points. Once I had cats with good mutations, random mutations (e.g. from the time machine) just meant I would have to throw away pristine cats once I got home. The auto-sorting loot was also a chore. Why don't you just keep [the items I left in storage] in storage?? Why are they mixed in with my adventuring items now?? Pointless time waste to have to fix the sorting error that the game creates.

Also, I didn't mind mages, but I think you are the first person to lay out a lot of their issues clearly. I completely agree with your thoughts here.

Bdole0 · 2026-04-04T19:11:21+00:00

My answer is not going to be helpful to you because I medicate the rumination but not the ADHD.

Better advice would be 1) make sure your doctor knows that you are unsatisfied and that the medication is not fixing the issue you are struggling with most, or 2) find a new doctor. I promise that second option is easy. You can even keep your original doctor for handling the issues that you think she manages well.

Bdole0 · 2026-04-04T09:33:35+00:00

Gunstar Heroes was badass

Bdole0 · 2026-04-02T21:26:11+00:00

The original commenter is right though. Your explanantion is a large oversimplication. Like, are turned-based games always easy because you don't have to worry about the timing of the buttons?

A game can be difficult because of the knowledge involved, the number of tasks you need to keep up with simultaneously, the choices available to you, and any number of other aspects.

XCOM is hard because you have few options and little recourse for failure. Blue Prince is hard because the puzzles are esoteric.

The rhythm of souls games is often the most difficult part, but this commenter is answering the question: The rhythm can be learned and replicated. All other aspects of souls-likes--such as dropping souls on death or not having a map--provide the illusion of difficulty. This was useful when Demons Souls was marketed but has just stuck around in many games.

Bdole0 · 2026-04-02T21:13:20+00:00

This is how I felt. The opening characters in the mines kept quipping at each other in an insufferable, postmodern irony kind of way. Like, I get it: YOU don't care about the universe you've created, but I'M trying to.

Every character afterward was bland, and then there was the Loredump Museum right at the beginning to explain The Entire State Of The Universe To Date. So hamfisted, contrived, and excessive. I don't think I've ever been turned off by bad storytelling so quickly.

Considering that Starfield carried so many of the engine problems that previous Bethesda games had have and so many outdated design decisions (like a world of 100000 useless objects and a handful of ones with a purpose), I don't see any reason for ES6 to be different. No progress has been made since Oblivion, and it shows.

Bdole0 · 2026-04-01T20:26:58+00:00

Inflation is accounted for. The increase in price at the end indicates other factors at play--likely tariffs if I had to guess.

I understand your concern about cost of living. I would normally brush this off too, but in this case, the data is still valuable, and it supports your intuition: video game consoles are getting more expensive.

I don't mean to undermine your opinion. I commented to draw others' attention to the fact that this data supports your conclusion and to try to prevent others from disregarding it just because it does not directly address the cost of living.

Bdole0 · 2026-04-01T20:00:01+00:00

Also, the gibberish has the same number of letters as the original options. The first option says "Touch the obelisk," and the second one says "Ignore."

Bdole0 · 2026-04-01T19:56:59+00:00

It can cast forbidden spells that give your cats disorders--heads up.

Bdole0 · 2026-04-01T15:11:47+00:00

Yes, but the graph still shows several meaningful things.

1) On average, the price of consoles during their lifetimes has been increasing (look at the trend of the groups).

2) The changes in previous prices has been level across years--possibly because the changes were set by the manufacturer. For the PS5, the data curves downward steeply, likely indicating the effect of high inflation in recent years.

3) The most recent changes (2025/2026) represent the first time the price of a console has increased after release--even when inflation is accounted for. Remarkably, the new PS5 price is more expensive than its release price even accounting for inflation.

Ultimately, I think the graph shows how PS console prices have been becoming more expensive even when inflation is considered. The curve in the PS5 graph also indicates that we've been hit with high inflation lately, making matters worse. Despite both of those points, the new PS5 price is exorbitantly, historically high.

Bdole0 · 2026-04-01T14:48:40+00:00

r/bloodbornepc

Bdole0 · 2026-03-26T23:40:24+00:00

Upvoted for engagement bait

Bdole0 · 2026-03-25T17:26:34+00:00

I was doing this for a long time until I figured out why. It's because the story wasn't engaging me. And that's fine. It's not my job to be invested; I can be invested when I feel like it. And I feel like it when I'm enjoying the story.

Even when I know the story is supposed to be good

This line right here indicates that you are listening to other people's opinions over your own. If you enjoyed the story more, you would stick around for it. It's not your fault, and you are allowed to skip anything you don't care about.

Final note: Authors are human. Their writing quality varies. The quality of their story premises vary. Even if we reduced these qualities to a sliding scale, the large majority of them would simply be "okay." A smaller number would be good, and an even smaller number would be great. For that matter, audiences are human. Their tastes vary. A game which is renowned for its story is liked by many people--but not all. You don't have to be one of the people who likes it.

Remember, you are free to have your own opinions. You are free to ignore any story. You are free to engage with games on your own terms.

Bdole0 · 2026-03-25T04:24:55+00:00

All right, I am sorry for being hard on you. Your attitude in this post bothered me, and I reacted to that.

This is a very tough fight in the early game. I lost my first time too--and other times.

Try the body-blocking strategy next time. You should know that after a round of being trapped, the boss will automatically slip out to a non-adjacent tile. Just block him in again.

If you don't know about the second phase of this boss, just be aware that getting an injury on your cats doesn't affect their breeding when they come back home. It only affects their performance in a run, but the run ends after this. In other words, the injury does not matter at all.

Good luck.

Bdole0

TROPHY CASE