## anonymous 5 years ago need help find the inverse of a 3x3 matrix

1. anonymous

1 2 0 0 3 -1 1 2 -1

2. anonymous

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

3. anonymous

i still cant figure it out :(

4. anonymous

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...

5. anonymous

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

6. anonymous

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.

7. anonymous

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

8. anonymous

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. :)

9. anonymous

what is the simplest way to find the determinant?

10. anonymous

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

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