Question

medals rewarded!
Find the inverse of the matrix, if it exists.
P=[4 4]
[1 -5]

Answer 1

to find the inverse of a two by two matrix \[
M=
\left[ {\begin{array}{cc}
a& b \\
c & d \\
\end{array} } \right]
\]
put
\[
M=
\frac{1}{ad-bc} \left[ {\begin{array}{cc}
d & -b \\
-c & a \\
\end{array} } \right]
\]

Answer 2

i.e. first find the determinant \(ad-bc\)

Answer 3

oops i should have written
\[M^{-1}=
\frac{1}{ad-bc} \left[ {\begin{array}{cc}
d & -b \\
-c & a \\
\end{array} } \right]\]

Answer 4

do you know how to find the determinant of your matrix?

Answer 5

you use the equation thing so well satellite...how do you do it!

Answer 6

i always resort to using the drawing tool but too messy

Answer 7

lol
google

Answer 8

google?

Answer 9

i forgot, so i googled "matrix in latex" there are lots of ways to do it, but i found a nice two by two example, cut and paste

Answer 10

btw you might know this, but if you want to see any code, right click and select "show math as" then "latex" and you can see it
good for copying too when answering a question

Answer 11

@bettni you following how to find the inverse? it is pretty easy for a two by two matrix, harder for others

Answer 12

i had no idea well i have no idea what code is...i think next semester we might be learning it but yea cheers for the advice

Answer 13

ohh i see

Answer 14

SIK

Answer 15

easy right?

Answer 16

I somewhat get it

Answer 17

first you need the determinant, because you have to divide by it

Answer 18

the determinant of \(
\left[ {\begin{array}{cc}
a& b \\
c & d \\
\end{array} } \right]\) is \(ad-bc\) which in your case is \(4\times( -5)-4\times 1=-24\)

Answer 19

so out front goes \(-\frac{1}{24}\)

Answer 20

then switch \(a\) and \(d\) and stick minus signs in front of \(b\) and \(c\)

Answer 21

\[M=
\left[ {\begin{array}{cc}
4& 4 \\
1& -5 \\
\end{array} } \right]\] the inverse is
\[M^{-1}=
-\frac{1}{24} \left[ {\begin{array}{cc}
-5& -4 \\
-1& 4 \\
\end{array} } \right]\]

Answer 22

so what answer choice would that be