Question

need help find the inverse of a 3x3 matrix

Answer 1

1 2 0
0 3 -1
1 2 -1

Answer 2

First, make sure you know the formula:
\[A^{-1}=\frac{1}{\det(A)}adj(A).\] Finding the determinant shouldn't be too difficult; but finding the adjugate matrix can be tricky. First, you want to take the transpose of A, and then find each element by determining the matrix of cofactors.

http://www.wikihow.com/Inverse-a-3X3-Matrix

Answer 3

i still cant figure it out :(

Answer 4

Have you been taught how to figure out the adjugate of a 3x3 matrix? If not, then you might have been meant to use a calculator. This isn't something they'd ask of someone without explicitly walking them through it first...

Answer 5

my math professor is really hard to follow. i mostly rely on the book to solve most of the material. however the book is hard to follow as well. i can solve a 2x2 matrix, but the book does not spend a lot of time on 3x3

Answer 6

Hm...okay, to find the adjugate, you have to first take the transpose of the matrix.
\[\left[ \begin{array}{cccc} 1 & 0 & 1 \\ 2 & 3 & 2 \\ 0 & -1 & -1 \end{array} \right].\] Now, replace each term with the determinant of the cofactors -- replace the first element with det[3,2;-1,-1], replace the second element with det[2,2;0,-1], etc. Then, you'll have the adjugate; and multiply by 1/det(A) to get the inverse.

Answer 7

ok
is that everything? I am following you so far.

Answer 8

I believe that's all you need to find the inverse; do you know how to find the determinant? If so, follow those steps for the adjugate and you should be fine; just use the empirical function I stated in my first response. :)

Answer 9

what is the simplest way to find the determinant?

Answer 10

Use the Rule of Sarrus:
http://en.wikipedia.org/wiki/Rule_of_Sarrus