Question

What is equal to the inverse of matrix N?

Answer 1

Augment the matrix by the identity matrix at the end, then apply row operations until you get the identity matrix at the beginning, and the rest of it will be the inverse

Answer 2

1/6

Answer 3

-6 -2 -6 -3

Answer 4

or alternatively
for \[M=\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\] \[M ^{-1}= \frac{ 1 }{ \det(m) }\left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]

Answer 5

is that correct?

Answer 6

i'll check now, sorry let me work it out

Answer 7

ok thank you

Answer 8

not quite, your 3 and 6 on the diagonal weren't negative so \[Inverse = \frac{ 1 }{ 6 }\left[\begin{matrix}6 & -6 \\ -2 & 3\end{matrix}\right]\]

Answer 9

Thank you!

Answer 10

no problem :)

Answer 11

I have one other question if you don't mind?

Answer 12

sure, if i can help i will

Answer 13

Solve the following system of equations using the inverse matrix method?
http://oi41.tinypic.com/2142q94.jpg

Answer 14

To be honest, I'm not familiar with the inverse matrix method in terms of solving a system of equations. Are you familiar with row reduction, or reduced echelon form?

Answer 15

oh okay actually, i have a method i've found that i can try and work through with you if you want?

Answer 16

So you need to set it up from the equations in terms of Ax=b where A is a matrix, x is a vector and b is the solution?
so
\[\left[\begin{matrix}1 & -4 \\ 8 & 1\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}-21 \\ 30\end{matrix}\right)\]

Answer 17

do you understand where that came from?

Answer 18

hmmm

Answer 19

no not really

Answer 20

so your equations are:
x-4y=-21
8x+y=30
okay if you think of a matrix like the first column is the x's, the second column is the y's
so if you take the coefficients of the x's and y's (the number in front) you get
\[\left[\begin{matrix}1 & -4 \\ 8 & 1\end{matrix}\right]\]

so the first row in the matrix is your first equation, where the first number is the number of x's, the second number is the number of y's, and the second row is just the same but for the second equation, right?

Answer 21

ok

Answer 22

do you understand that fully first, before i move on?

Answer 23

yes I believe I do

Answer 24

great! okay then so, the \[\left(\begin{matrix}x \\ y\end{matrix}\right)\] i got next is just the values of the equation that you are trying to solve (ie you want to find what x and y are)
and the bit at the end is just the solution given in the equations

okay?

Answer 25

Okay!

Answer 26

good okay so back to the equation i wrote before \[\left[\begin{matrix}1 & -4 \\ 8 & 1\end{matrix}\right]*\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}-21 \\ 30\end{matrix}\right)\] okay?

Answer 27

okay!

Answer 28

okay so the whole concept of the inverse matrix method is to take the inverse of the 2x2 matrix and multiply both sides by it so: where we have
Ax=b
you want to work out the inverse of A (ie the 2x2 matrix)
so let me know what you get for that

Answer 29

-3 , -6?

Answer 30

so you should get 4 entries again, like the last example, it's exactly the same method

Answer 31

wait

Answer 32

for the final answer?

Answer 33

oh where they the final solutions you gave me, for x and y? sorry i was a bit behind then, you're a step ahead of me if so, give me a sec lol

Answer 34

oh sorry lol

Answer 35

don't apologise! it's good to be ahead lol! your values are correct, but they should both be positive, not negative

Answer 36

ohhh ok so those are the right numbers @sarahusher

Answer 37

yes they are!

Answer 38

Thanks again for everything :)

Answer 39

not a problem dear, good work!

Answer 40

thank you!