Question

Determine whether the matrix has an inverse. If an inverse exists, find it. matrix: -5 -18 2 7

Answer 1

inverse exists if determinant is not 0. inverse matrix is given by 1/ad-bc [[d,-b][-c,a]]

Answer 2

all i see is a bunch of letters..

Answer 3

\[
\begin{pmatrix}
-5 & -18 \\
2 & -4
\end{pmatrix}
\]
like that?

Answer 4

YES!

Answer 5

whatever it is, you need to see if the matrix has an inverse before you start to find it
do you know how to take the determinant? you need that

Answer 6

but where did you get the negaticve 4 fromm?

Answer 7

no i don't.

Answer 8

\[\begin{pmatrix}
-5 & -18 \\
2 & 7
\end{pmatrix}\]

Answer 9

is that the one?

Answer 10

yessss.

Answer 11

ok determinant of
\[\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}\]
is \(ad-bc\) find that first

Answer 12

okayy im writing it down. you can keep going.

Answer 13

let me know what you get, then we can continue

Answer 14

wait im lost... how can you subtract that?

Answer 15

inverse of \[\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}\] is easy to find (harder the bigger the matrix)
it is
\[\frac{1}{ad-bc}\begin{pmatrix}
d & -b \\
-c & a
\end{pmatrix}\]

Answer 16

\[a=-5,b=-18, c=2,d=7\] you compute
\[(-5)\times 7-(-18\times 2)\]

Answer 17

okayyy

Answer 18

i got 1..

Answer 19

yes

Answer 20

which makes it even easier
if the determinant is 0 there is no inverse

Answer 21

to find the inverse use the rule i gave above, but you don't have to divide by the determinant because dividing by 1 is like doing nothing

Answer 22

ohh, so its not posssible.. it doesn;'t exist?

Answer 23

no it exists alright

Answer 24

if the determinant was 0 it would not exist

Answer 25

but since the determinant is 1 it does exist

Answer 26

here is the formula
\[\frac{1}{ad-bc}\begin{pmatrix}
d & -b \\
-c & a
\end{pmatrix}\]

Answer 27

but since \(ad-bc=1\) all you need is
\[\begin{pmatrix}
d & -b \\
-c & a
\end{pmatrix}\]

Answer 28

so im multiplying everything by one?

Answer 29

is it clear what you have to do?

Answer 30

multiplying by one is like doing nothing, so no don't "multiply by one?"

Answer 31

welll no i don't understand haa. im still lost. im sorrry.

Answer 32

this is what you need
\[\begin{pmatrix}
d & -b \\
-c & a
\end{pmatrix}\]
with
\[a=-5,b=-18, c=2,d=7\]

Answer 33

wait! so your saying its gonna be 5,-18, -2,7? or am i still way off?

Answer 34

the inverse of a matrix is given by 1 over determinant times adjugate matrix, which for 2x2 matrix is \[\left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]

Answer 35

so u swap position of a and d and make b and c the opposite sigsn

Answer 36

sooo idk how to do the matrix box but its gonna be 7 -18 -2 and -5?