SOLUTION: Evaluate the determinant |c2 a| |-a c| Please show all work Thank You

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Evaluate the determinant |c2 a| |-a c| Please show all work Thank You      Log On


   

Question 119266: Evaluate the determinant
|c2 a|
|-a c|
Please show all work
Thank You
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The determinant of a 2x2 matrix, A, given by,
[A]=%28matrix%282%2C2%2Ca%5B1%5D%2Ca%5B2%5D%2Ca%5B3%5D%2Ca%5B4%5D%29%29
is given by
abs%28A%29=a%5B1%5Da%5B4%5D-a%5B2%5Da%5B3%5D
In your case,
[M]=%28matrix%282%2C2%2Cc%5E2%2Ca%2C-a%2Cc%29%29
a%5B1%5D=c%5E2 I assume that's what you meant and not 2c.
a%5B2%5D=a
a%5B3%5D=-a
a%5B4%5D=c
and then
abs%28M%29=a%5B1%5Da%5B4%5D-a%5B2%5Da%5B3%5D
abs%28M%29=c%5E2%28c%29-a%28-a%29
abs%28M%29=c%5E3%2Ba%5E2