Question

Please help! Use an inverse matrix to solve each equation or system. Equation in reply.

Answer 1

\[\left[\begin{matrix}4 & 1 \\ 2 & 1\end{matrix}\right]\left[\begin{matrix}x \\ y\end{matrix}\right]=\left[\begin{matrix}10\\ 6\end{matrix}\right]\]

Answer 2

@pooja195 @Michele_Laino @triciaal @jigglypuff314

Answer 3

@Caseyyyy15 I can try to help you :)
although I am not very good a matrices so I might make a mistake...
let's first try to find the inverse matrix of
\[\left[\begin{matrix}4 & 1 \\ 2 & 1\end{matrix}\right]\]do you know how to do that? :)

Answer 4

is it the 1/ad-bc thing? and don't worry I'm awful too! :)

Answer 5

yeah, it's that :)

Answer 6

\[\left[\begin{matrix}.5 & -.5 \\ -1 & 2\end{matrix}\right]\] is this right for the inverse?

Answer 7

yep! great job!
now we multiply that by
\[\left(\begin{matrix}10 \\ 6\end{matrix}\right)\]

Answer 8

do you know how to do that? :)

Answer 9

on my calculator yes, but I'm needing to show work, how do you do it with the 2x1..

Answer 10

i know how to do it if they were both 2x2 matrices

Answer 11

it's an idea called the "dot product"
https://www.mathsisfun.com/algebra/matrix-multiplying.html
\[\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\left(\begin{matrix}e \\ f\end{matrix}\right) = \left(\begin{matrix}(a*e + b*f) \\ (c*e + d*f)\end{matrix}\right)\]

Answer 12

okay is it.. \[\left(\begin{matrix}2 \\ 2\end{matrix}\right)\]

Answer 13

yep!
that's what I got too :)
(hopefully it's right) *crosses fingers* :3

Answer 14

lol so is that the final answer??\[\left(\begin{matrix}x \\ y\end{matrix}\right)\] I've never seen the x and y thing so it freaked me out!

Answer 15

yeah the 2 2 is the final answer :)

I used this as a guide: http://www.classzone.com/eservices/home/pdf/student/LA204EAD.pdf

Answer 16

wow okay! thanks so much! :)
Do you think you could help me with one more?

Answer 17

sure, I can try :)

Answer 18

is how it looks on my paper and its the same instructions

Answer 19

then you would get the matrix problem:
\[\left[\begin{matrix}1 & 2\\ 2& 4\end{matrix}\right]\left[\begin{matrix}x\\ y\end{matrix}\right]=\left[\begin{matrix}15 \\ 30 \end{matrix}\right]\]

Answer 20

*blinks*
oh wait

Answer 21

the 1/(ad - bc) would get you 1/0
that would mean that they are the same equation
aka infinitely many solutions

Answer 22

i thought it made since until you said that. I'm confused now..

Answer 23

what are you getting the inverse of to start?

Answer 24

try doing the 1/(ad - bc)
I got one divided by zero
from just that

but it is impossible to divide by zero

Answer 25

oh from the equation you got okay one sec

Answer 26

i got zero too! so is it no solution?

Answer 27

it's infinitely many solutions
because they are the same equation

Answer 28

interesting okay thank you so much! You rock!

Answer 29

I'm glad I could help ^_^