Question 962323
give the determinant {{{matrix(3,3,5, 4, 2, 1, 7, 3, 4, -1, 1)}}} (write the minor of element {{{3}}} and write down co-factor of element {{{3}}}.

The minor of the {{{3}}} in the row {{{2}}} is the {{{2*2}}} determinant which contains only the elements of determinant that are NOT in the same row or the same column (which is column {{{3}}}) as that {{{3}}}.


  	
{{{matrix(3,3,5, 4, 2, 1, 7, 3, 4, -1, 1)}}}
	
 	
The minor of that {{{3}}} is this determinant:
 
{{{matrix(2,2,5, 5, 4, -1)}}}	= {{{5(-1) - 4(5) = -5 -20 = -25}}}


As you can see, the minor for row {{{2}}} and column {{{3}}} is {{{M23 = -25}}}.


The cofactor is {{{-1}}} times minor {{{-25}}};so, it is {{{25}}}