Question

wondering if these equations will form a linear system and if yes will there be no solution or one or many solutions?

3z + x = -4
y + 5z = 1
6x + 2z = 3
-x -y -z = 4

Answer 1

in linear algebra it should look like
\[\left[\begin{matrix}1 & 0 & 3 \\ 0 & 1 & 5 \\ 6 & 0 & 2 \\ -1 & -1 & -1 \end{matrix}\right]\cdot \left(\begin{matrix}x \\ y \\ z \end{matrix}\right) = \left(\begin{matrix}-4 \\ 1 \\ 3 \\ 4 \end{matrix}\right)\]
you have to find out if the matrix has full rank. if so look in a linear algebra book about solvability.
(tip: gaussian algorithm)

Answer 2

mmm mind if you can explain when will equations form a linear system?

Answer 3

hmm, i don't really know what to say. "when its linear" but this wouldn't help you.
a funktion \(f\) is linear if
\[ f (a + b) = f(a) + f(b) \]and
\[ f( a \cdot b ) = f(a) \cdot f(b) \] and a linear system is the funktion that solves the equations, and is linear.
does that help you?

Answer 4

mm well one thing im trying to understand is can a set of equations have difference variables or it has to have same variables to become a linear sytem. for e.g
will 2x - 4y = 2
2x - 4y + 5z = 5
be a linear system if the first one has 2 unknowns and second one has 3

Answer 5

\[2x - 4y + 0z = 2 \]\[2x - 4y + 5z = 5 \]here its easy you can set z to \(3/5\)

Answer 6

alright i see

Answer 7

well thanks gonna post another questions :P

Answer 8

you're welcome. please mark me as good.
i just started with openstudy, i like it.

Answer 9

what about x1 + x2 = x3 + x4?
I think it will form a linear system and since it has one unknown then it will have infinite solutions right?

Answer 10

sorry im wrong it has 4 unknowns

Answer 11

yeah if you want to solve linear problems pretty easy. use matrices.
like i did in my first post. it's pretty easy.
but i must go now. i hope i could help you.