Question 979883


Since the matrix contains zero in the first row, &nbsp;I will use &nbsp;<B><U>cofactoring the determinant along the first row</U></B>&nbsp; (see the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Co-factoring-a-3x3-determinant.lesson>Co-factoring the determinant of a 3x3 matrix</A> in this site):


det {{{(matrix(3,3, 4,0,-1, 3,6,-2, -2,5,1))}}} = 4*det{{{(matrix(2,2, 6,-2, 5,1))}}} - 0*det{{{(matrix(2,2, 3,-2, -2,1))}}} + (-1)*det{{{(matrix(2,2, 3,6, -2,5))}}} = 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 4*det{{{(matrix(2,2, 6,-2, 5,1))}}} + (-1)*det{{{(matrix(2,2, 3,6, -2,5))}}} = 4*(6*1 - 5*(-2)) - (3*5 - (-2)*6) = 4*(6 - (-10)) - (15 - (-12)) = 4*(6 + 10) - (15 + 12) = 4*16 - 27 = 64 - 27 = 37.