Question

Write the system {2y+7z= -3, -3x-3y=3, 7x-8z=3} as a matrix equation
@satellite73 @phi @thomaster
Someone please help?????

Answer 1

list your variables in alphabetical order: x,y,z and make them into a vector
\[\left[\begin{matrix}x \\ y \\ z\end{matrix}\right]\]

Answer 2

x y z c
0 2 7 -3
-3 -3 0 3
7 0 -8 3

Answer 3

now put a matrix on the left side of that vector.
each row of the matrix will be one equation. It will multiply the vector of variables
For example
2y+7z= -3

notice that this is the same as 0*x + 2*y +7*z = -3
the row of the matrix will 0 2 7

Answer 4

okay thank you so much!! I think I get it now :)

Answer 5

on the other side of the equal sign will be a vector of the "constants"

Answer 6

\[\left[\begin{matrix}0 & 2 & 7 \\ ? & ? & ? \\ ? & ? & ?\end{matrix}\right]\left[\begin{matrix}x \\ y \\ z\end{matrix}\right]= \left[\begin{matrix}-3 \\ ? \\ ?\end{matrix}\right]\]

Answer 7

[0 2 7] [x] [-3]
[-3 -3 0] [y] = [3]
[7 0 -8] [z] [3] ??? is this right?

Answer 8

yes, looks good.

Answer 9

If you know how to multiply a matrix times a vector, you can "re-create" the equations

on the other hand, once you have a matrix form, you can use all the tools of linear algebra to solve these equations.

Answer 10

Thank you so much! I appreciate all your help