Question

can someone please explain to me why you can work out 3 (or more) unknowns with matrices?

Answer 1

if u have the same no of equtions a matrix can be used to solve for 3 or more than three variables easily

Answer 2

You have to have at least as many equations as variables. Then just do the regular processes.

Answer 3

yeah but why does that work?

Answer 4

its just like solving a system of equations, as long as num of unknowns matches the num of equations there is a possibility of a solution

Answer 5

its just a more efficient way of solving by substitution or elimination

Answer 6

...

i know /what/ it is
i know /where/ to use it

but /why/ does it work?

Answer 7

hmm it works i guess because by using matrix operations you can transform a system of equations into x1 = a, x2=b, x3=c, etc...

Answer 8

For example, for 3 unknown variables and 3 equations, each equation represents a plane and where all 3 planes intersect that is the solution.
Same as for two variables, that's just two lines intersecting.
For higher number of variables it cannot be visualized, but it's just an extension of those.

Answer 9

Now that I've posted and read it, I don't know if that's really an explanation or if it just adds more confusion.

Answer 10

and with... 4 or more unknowns its that many planes, and what? when you can make as many equations as unknowns, its like haveing that many planes, that can only intersect at one point? is that why it works? because there is only ever one possible solution with a particular number of equations?

Answer 11

I don't think it's just more planes, because more variables would also mean more dimensions. That's what I mean by: 'it cannot be visualized'
Unless you can think in more than 3 dimensions.

Answer 12

ok... so say im not trying to think in # dimensions..

but i have # equations and # unknowns..

then i can use both of them, and using matrices is a way of using # dimensions, to work out where, when i have # equations, the # equations will 'meet' and only ever give me one possible solution for each variable?

so like

5x +5y = 3
6x+ 7y = 4

does that mean if i wanted to 'solve for x and y' i will only ever get one value of x and one value of y, with those two equations?

Answer 13

Right. In this case, the (x,y) coordinates where the two lines meet.

Answer 14

For 3 variables it's 3 planes meeting in 3D space.
And that's where it ends. For more variables, you just do the methods and solve them and don't think about what they represent in real life because you can't and you'll get a headache.

That's the limit of my understanding anyway, you might do a google search and find a better description.

Answer 15

nah i think this is better, cause i got a live reply, and one that i could understand too

Answer 16

do you think with more dimensions, you would just describe it as where (dimensions minus one) meet in space?

so for 4 unknowns (say the fourth dimension is time)

with four unknowns you can use matrices to solve your problem by getting a matrix to model 4, three dimensional objects and where they meet on that fourth dimension?

hm i didnt even use the dimensions' names. oh well.