Question

Help?

Determine whether each matrix has an inverse. If an inverse exists, find it.

[ 4,8_-3,-2]

Answer 1

@phi ?

Answer 2

does the det=0?

Answer 3

no?

Answer 4

\[\huge \left[\begin{matrix}4 & 8 \\ -3 & -2\end{matrix}\right]\]
This matrix?

Answer 5

Well, anyway, two things to keep in mind... if the determinant of a matrix is not zero, then it will have an inverse.

Second, and importantly, since this is just a 2x2 matrix, there is a straightforward way of getting its inverse...
So, suppose we have an (invertible) 2x2 matrix...
\[\huge \left[\begin{matrix} a & b \\ c & d\end{matrix}\right]\]
Then the quickest way to get its inverse is using this formula...
\[\huge \frac1{ad-bc}\left[\begin{matrix} d & -b \\ -c & a\end{matrix}\right]\]

Answer 6

So [2,3_-4,-8] @terenzreignz

Answer 7

no, maybe try using the identity method instead of matrix of cofactors

Answer 8

Im not sure how to do that?

Answer 9

ok so you want to set up a matrix where on the left you have your matrix and then on the right you have the identity matrix

Answer 10

ie.
\[\huge \left[\begin{matrix} a & b & 1 & 0 \\ c & d & 0 & 1\end{matrix}\right]\]

Answer 11

then using row reductions, get the identity on the left instead

Answer 12

Ok so this does have an inverse??

Answer 13

do you really think I'd have you doing all of this if it didn't? And since you told me the \(det \not= 0\) then there does exist an inverse

Answer 14

the inverse is [-2,3_-8,4]?