Question

Use an inverse matrix to solve the system of linear equations.
Will give a medal! :) really need help!

Answer 1

\[\frac{ 1 }{ 2 }x + y= -1\]
\[2x+8y= -20\]

What is the inverse matrix??

\[A ^{-1}\]= ( __ __)
__ __

Answer 2

@genius12

Answer 3

doing it now

Answer 4

are you sure this has an inverse? its not a nxn matrix

Answer 5

Sure it is :)
Remember
\[\huge A=\left[\begin{matrix}\frac12 & 1 \\ 2 & 8\end{matrix}\right]\]
\[\huge b=\left[\begin{matrix}-1 \\ 20\end{matrix}\right]\]
\[\huge z= \left[\begin{matrix}x \\ y \end{matrix}\right]\]
so, you can say
\[\huge Az=b\]
A is a 2x2 matrix, so...
\[\huge z=A^{-1}b\]

Answer 6

ohhh yea, forgot thats b. completely left my memory unit now. helped me out too

Answer 7

Do you know about Second Partial Derivative Tests?

Answer 8

I don't know why they're made to use inverses when using determinant seems much easier... in any case...
\[\huge A^{-1}=\left[\begin{matrix}4 & -\frac{1}{2} \\ -1 & \frac14\end{matrix}\right]\]

Answer 9

i'll give you a medal, you helped jog my memory

Answer 10

the poster is probably knocked out sleep

Answer 11

The question isn't answered yet, but the poster now has the necessary tools to do it :)
I'm hoping the poster will ask how to get the inverse :D

Answer 12

@terenzreignz hello um also part of this question asks,
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution of the system is x=__ and y=__
b. there are infinitely many solutions
c. there is no solution.

Answer 13

@Hero