Question

I am confused on how to go about doing this. Linear algebra question for homework

Answer 1

HI!!

Answer 2

Hello

Answer 3

one way to do it would be to multiply the matrix on the right by the inverse of the matrix on the left

Answer 4

\[AB=C\iff A=CB^{-1}\]

Answer 5

oh ok

Answer 6

let me try that i'll respond once I have done that

Answer 7

inverse of a 2 by 2 matrix is easy to find right?

Answer 8

yes

Answer 9

\[\begin{pmatrix} x & y \\ z & v \end{pmatrix}^{-1}=\frac{1}{D}\begin{pmatrix} v & -y \\ -z & x \end{pmatrix}

\]

Answer 10

course you can always cheat too, not really necessary

Answer 11

https://www.wolframalpha.com/input/?i=%7B%7B2%2C4%7D%2C%7B2%2C5%7D%7D%5E%28-1%29

Answer 12

so the inverse would be \[\left[\begin{matrix}2.5 & -2 \\ -0.5 & 0.5\end{matrix}\right]\] right?

Answer 13

or have i done it wrong?

Answer 14

looks good

Answer 15

oh no

Answer 16

the -5 is wrong

Answer 17

that should be -1

Answer 18

-5?

Answer 19

first get \[\begin{pmatrix} 5& -4 \\ -2 & 2 \end{pmatrix}\]

Answer 20

the divide all by 2

Answer 21

oh wait i know what u mean lol, that was my mistake

Answer 22

i thought the 2 were 1s

Answer 23

lol

Answer 24

\[\begin{pmatrix} 2.5& -2 \\ -1 & 1 \end{pmatrix}\]

Answer 25

i think that is right

Answer 26

yes, that is, so now I just have to multiply that by the resultant in the question correct?

Answer 27

should work
i got this
https://www.wolframalpha.com/input/?i=%7B%7B2%2C7%7D%2C%7B0%2C5%7D%7D.%7B%7B2.5%2C-2%7D%2C%7B-1%2C1%7D%7D

Answer 28

ok, ill do it, and see if i got that on paper

Answer 29

ok good luck!\[\color\magenta\heartsuit\]

Answer 30

yup i got the same answer, Thank you so much for your help.
:D