SOLUTION: find the determinant of the matrix {{{(matrix(2,2,5, 2, -3, 1))}}}

Algebra ->  Matrices-and-determiminant -> SOLUTION: find the determinant of the matrix {{{(matrix(2,2,5, 2, -3, 1))}}}       Log On


   

Question 172192: find the determinant of the matrix %28matrix%282%2C2%2C5%2C+2%2C%0D%0A++++++++++++++++++++++++++++++++++++-3%2C+1%29%29

Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The determinant of the general 2x2 matrix %28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29 is D=a%2Ad-b%2Ac


So in this case, the matrix %28matrix%282%2C2%2C5%2C2%2C-3%2C1%29%29 gives us the values a=5, b=2, c=-3, and d=1


D=a%2Ad-b%2Ac Start with the determinant of any 2x2 matrix


D=5%2A1-2%2A%28-3%29 Plug in a=5, b=2, c=-3, and d=1


D=5%2B6 Multiply


D=11 Add


So the determinant of the matrix %28matrix%282%2C2%2C5%2C2%2C-3%2C1%29%29 is 11

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

The determinant of matrix %28matrix%282%2C2%2CA%2CB%2CC%2CD%29%29 is writen
just like the matrix except it is enclosed within vertical bars
instead of parentheses or brackets:

abs%28matrix%282%2C2%2CA%2CB%2CC%2CD%29%29

The rule for finding the value of the determinant is

abs%28matrix%282%2C2%2CA%2CB%2CC%2CD%29%29=AD-BC

Therefore, the determinant of

%28matrix%282%2C2%2C5%2C2%2C-3%2C1%29%29

is 

abs%28matrix%282%2C2%2C5%2C2%2C-3%2C1%29%29 

and its value is:



Edwin