[MATLAB] 3*3 역행렬

k =
 
[ a, b, c]
[ d, e, f]
[ g, h, i]
 
 
>> k^-1  % k의 역행렬.
 
ans =
 
[   (e*i-f*h)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e),  -(b*i-c*h)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e), -(-b*f+c*e)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e)]
[  -(d*i-f*g)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e),   (a*i-c*g)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e),  -(a*f-c*d)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e)]
[ -(-d*h+e*g)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e),  -(a*h-b*g)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e),   (a*e-b*d)/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e)]
 
 
>> ans.*(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e)
 
ans =

 
[  e*i-f*h, -b*i+c*h,  b*f-c*e]
[ -d*i+f*g,  a*i-c*g, -a*f+c*d]      
[  d*h-e*g, -a*h+b*g,  a*e-b*d]

 

 

 

결론

k = 
[ a, b, c]
[ d, e, f]
[ g, h, i]

 

 k^-1 =

	[  e*i-f*h,    -b*i+c*h,      b*f-c*e]
1/(a*e*i-a*f*h-d*b*i+d*c*h+g*b*f-g*c*e)	[ -d*i+f*g,     a*i-c*g,    -a*f+c*d]
	[  d*h-e*g,  -a*h+b*g,    a*e-b*d]