Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Given a 3 x 3 matrix:

$$ A= \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix} $$

Can $A^{-1}$ be shown as as a 3x3 matrix with each element in terms of $a,b,c,d,e,f,g,h$ and $i$. Showing basic operators (only $+ - / *$)?

share|improve this question
1  
see [en.wikipedia.org/wiki/… –  martini May 22 '13 at 14:43

1 Answer 1

up vote 6 down vote accepted

$$A^{-1}=\frac{1}{\det(A)} adj(A)$$

$$\det(A)=aei+dhc+bfg-ceg-bdi-afh$$

$$adj(A)= \begin{bmatrix} ei-fh & ch-bi & bf-ce \\ fg-di & ai-cg & dc-af \\ dh-ge & bg-ah & ae-bd \\ \end{bmatrix}$$

_

share|improve this answer
    
+1 Nice one @N.S. –  dreamer May 22 '13 at 14:49

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.