/sci/ - Science & Math

So what happened to B1056?

Is SUSY real or just a meme?

When will we find the first supersymmetric particle?

>>9650709
>Chickens are not a human social role

Why do you hate transpecies people?

>>9639509
>When there is a procedure to perfectly switch the sex of a mature human male.
When might such a procedure be developed?
Asking for a friend.

Is it worth it to so a second major, if I'm going to graduate two years later?

>>9190590
Give us an example of a proof you have trouble with. I'll try to explain it to you.

Since there is no charge or current in vacuum, why do electromagnetic waves exist in a vacuum?
What is generating these electromagnetic waves?

>human beings having seemingly having deific powers of the mind

>>8832584
bump

>>8812444
Somebody, please explain the joke?

>>8784484

My question has to do with the concept of dimension or "direction in space", more specifically, when considering a linear system as a system of equations compared to a linear combination of vectors.

I guess specifically what I'm curious about is, given an arbitrary linear system, why is the concept of direction in space sort of contained / stored in the variables when considering the system as linear equations, but then is stored in the vectors when considering the same system as a linear combination of vectors?

I know its sort of a strange question, so I'll phrase it using a more concrete yet still general example. Consider a linear system of three equations in three variables, where each equation is of the form (a_i)x + (b_i)y + (c_i)z = d_i. For convenience, and so that we may get some nice geometric intuition, suppose also they represent three distinct planes in R^3 (so we have linear independence). In the context of the system representing planes in space, it seems to me that dimension/direction is sort of "stored" in the variables x, y and z. Now this same system of 3 equations in 3 unknowns can also be expressed as a linear combination of vectors: x<a_1, b_1, c_1> + y<a_2, b_2, c_2> + z<a_3, b_3, c_3>. Here direction of course is stored in the vectors themselves; the three variables that stored direction in the context of linear equations now simply scale the vectors.

And it gets even more bizarre when you consider that, considering the system as linear equations of planes in R^3, we can express each plane as a vector equation by dotting any vector parallel to it with the normal and setting it equal to zero!

Why is the moon landing questioned? What would be the reason to fake it? Not even the soviets question it.