SOLUTION: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show

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Question 30198: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work
A square matrix is lower triangular if every entry above the diagonal is 0.
a. Give an example of a 3x3 lower triangular matrix.
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.
c. Show algebraically that the determinant of a 2x2 lower triangular matrix will always be the product of the entries on the diagonal.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
a. Give an example of a 3x3 lower triangular matrix.
(A)=matrix%283%2C3%2C1%2C0%2C0%2C2%2C3%2C0%2C2%2C1%2C2%29
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%282%2C2%2Ca%2C0%2Cb%2Cc%29
|B|= a*c-0*b=ac
PRODUCT OF DIAGONAL ELEMENTS =a*c = ac =|B|