Given:
#-2[(-1,0), (1,4)]-(-1)[(-2,3), (0,4)]+4[(-2,2), (1,-1)]#
We know that this will give us a #2xx2# matrix, #[(a_(1,1), a_(1,2)),(a_(2,1), a_(2,2))]#:
#-2[(-1,0), (1,4)]-(-1)[(-2,3), (0,4)]+4[(-2,2), (1,-1)] = [(a_(1,1), a_(1,2)),(a_(2,1), a_(2,2))]#
Multiply every element of the first matrix by -2:
#[(2,0), (-2,-8)]-(-1)[(-2,3), (0,4)]+4[(-2,2), (1,-1)] = [(a_(1,1), a_(1,2)),(a_(2,1), a_(2,2))]#
The #- (-1)# in front of the second matrix becomes a #+#:
#[(2,0), (-2,-8)]+[(-2,3), (0,4)]+4[(-2,2), (1,-1)] = [(a_(1,1), a_(1,2)),(a_(2,1), a_(2,2))]#
Multiply every element of the third by 4:
#[(2,0), (-2,-8)]+[(-2,3), (0,4)]+[(-8,8), (4,-4)] = [(a_(1,1), a_(1,2)),(a_(2,1), a_(2,2))]#
The rules of matrix addition are that you add up the corresponding elements of the matrix:
#a_(1,1) = 2 - 2 -8 = -8#
#[(2,0), (-2,-8)]+[(-2,3), (0,4)]+[(-8,8), (4,-4)] = [(-8, a_(1,2)),(a_(2,1), a_(2,2))]#
#a_(1,2) = 0+3+8 = 11#
#[(2,0), (-2,-8)]+[(-2,3), (0,4)]+[(-8,8), (4,-4)] = [(-8, 11),(a_(2,1), a_(2,2))]#
#a_(2,1) = -2+0+4 = 2#
#[(2,0), (-2,-8)]+[(-2,3), (0,4)]+[(-8,8), (4,-4)] = [(-8, 11),(2, a_(2,2))]#
#a_(2,2) = -8+4-4 = -8#
#[(2,0), (-2,-8)]+[(-2,3), (0,4)]+[(-8,8), (4,-4)] = [(-8, 11),(2, -8)]#
