Question 30198
a. Give an example of a 3x3 lower triangular matrix.
(A)={{{matrix(3,3,1,0,0,2,3,0,2,1,2)}}}

b. Using your example from part (a), show that the determinant of a lower triangular matrix is the product of the entries on the diagonal.
|A|=1(3*2-0*1)-0+0 =6
PRODUCT OF DIAGONAL ELEMENTS =1*3*2=6 =|A|
c. Show algebraically that the determinant of a 2x2 lower triangular matrix will always be the product of the entries on the diagonal.

LET (B) = {{{matrix(2,2,a,0,b,c)}}}
|B|= a*c-0*b=ac
PRODUCT OF DIAGONAL ELEMENTS =a*c = ac =|B|