document.write( "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\r
\n" ); document.write( "\n" ); document.write( "A square matrix is lower triangular if every entry above the diagonal is 0.
\n" ); document.write( "a. Give an example of a 3x3 lower triangular matrix.
\n" ); document.write( "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.
\n" ); document.write( "c. Show algebraically that the determinant of a 2x2 lower triangular matrix will always be the product of the entries on the diagonal.
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Algebra.Com's Answer #16903 by venugopalramana(3286)\"\" \"About 
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a. Give an example of a 3x3 lower triangular matrix.
\n" ); document.write( "(A)=\"matrix%283%2C3%2C1%2C0%2C0%2C2%2C3%2C0%2C2%2C1%2C2%29\"\r
\n" ); document.write( "\n" ); document.write( "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.
\n" ); document.write( "|A|=1(3*2-0*1)-0+0 =6
\n" ); document.write( "PRODUCT OF DIAGONAL ELEMENTS =1*3*2=6 =|A|
\n" ); document.write( "c. Show algebraically that the determinant of a 2x2 lower triangular matrix will always be the product of the entries on the diagonal.\r
\n" ); document.write( "\n" ); document.write( "LET (B) = \"matrix%282%2C2%2Ca%2C0%2Cb%2Cc%29\"
\n" ); document.write( "|B|= a*c-0*b=ac
\n" ); document.write( "PRODUCT OF DIAGONAL ELEMENTS =a*c = ac =|B|
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