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Linear Algebra Questions
lucas215
Registered User new member
Registered User new member
Hello
I was just wondering if anybody out there knows a lot about linear algebra. I have two short proofs that I am having problems with. They don't seem that difficult, but for some reason I am having problems with them. If I get any responses to this post, I can put the problems up so everyone can see. They deal with the topics of one-to-one, onto, and subspaces. Thanks everyone.
Lucas
I was just wondering if anybody out there knows a lot about linear algebra. I have two short proofs that I am having problems with. They don't seem that difficult, but for some reason I am having problems with them. If I get any responses to this post, I can put the problems up so everyone can see. They deal with the topics of one-to-one, onto, and subspaces. Thanks everyone.
Lucas
lucas215 on
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(-8)² = 64
-(8)² = -64
How do the parentheses change the way you would out the problem?
So -(8)² is -8^-2 which is -8*-8 and -(8)² is just -8*8?
Edit: So what happened to OP asking about linear algebra?
So I think I figured it out, -8² is just a short way of writing -(8*8). That makes sense to me.
(-8)² would be -8*-8 right?
When looking at exponents I have to think of them as being in parentheses, or just use the order of operations?
EDIT: Always use order of operations. Exponentiation comes before subtraction. Brackets come before exponentiation.
It's a useful mnemonic and sounds like a sci-fi robot name.
Google poked at it and came up with "-((-(-1)) - (-3)) = -4". Google is pretty smart, so it's probably right. If you can wrap your brain around it (which I can't with how sleepy I am, so I'm no help there), you might be able to solve the mysteries of the universe.
edit: I worked it out on paper and did it in this order:
-(- -1 - -3)
-(1 + 3)
The --1 means do the opposite, so the -1 becomes 1. Then change the - between 1 and 3 to a plus and turn the -3 to positive.
-1 + -3
Magical opposite brackets!
-4
And past that it's pretty straightforward. I may have messed up somewhere so hopefully someone will check it independently.
edit: I got the order wrong in the post, but it all makes sense on paper where I did all the steps on paper rather than in my head.
edit: I got confused after the magic opposite bracket. Now it all seems to make sense.
Basically, move slowly and break problems down into components to make it less of a headache.
(- -) something as ( + ) something,
Also, I am currently taking LinAlg, my final is in a couple hours, and I dealt with all the topic's you're talking about. If you wanna thrown down the question, I'll be happy to look at it tomorrow, and try and solve it (mind you, I'm not the greatest at it).
Also, 99% of the time, when people write down numbers negatives to exponents, they rarely take the time to place draw parenthasis around the negative and the number. But that's usually what they're implying.
However, from what I'm gathering, you're just learning about them, so the math teacher is trying to enforce the idea that -8^2, is really, 8^2, with a negative in the front.
But generally, in most math classes (at least the one's I've taken, and I'm taking quite a few at the moment (Engineering FTW
So, don't get fustrated over what you're being taught. Just try and keep in mind, that the generally accepted form right now, is not actually the accepted form
Edit: Wow, I just reread what I wrote, and that made MINIMAL sense. If it doesn't make sense, or confuses you, just ignore it. I'll correct it tomorrow after some sleep