SOLUTION: Solve the following equation. |0 0 -1| |3 x 0 | = x^2 |2 0 3 | Please help! I have no idea how to do this!

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve the following equation. |0 0 -1| |3 x 0 | = x^2 |2 0 3 | Please help! I have no idea how to do this!      Log On


   

Question 762565: Solve the following equation.
|0 0 -1|
|3 x 0 | = x^2
|2 0 3 |
Please help! I have no idea how to do this!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

|0 0 -1|
|3 x 0|= x%5E2
|2 0 3|
use the rule
|a b c|
|d e f|= =a(ei-hf)-d(bi-hc)+g(bf-ec)
|g h i|
so,

+0%283x%29-0%289%29-1%280-2x%29=x%5E2
2x=x%5E2
0=x%5E2-2x
0=x%28x-2%29
x=0 or x=2
check:
0%280%2A3-0%2A0%29-3%280%2A3-0%2A%28-1%29%29%2B2%280%2A0-0%2A%28-1%29%29=0
0%282%2A3-0%2A0%29-3%280%2A3-0%2A%28-1%29%29%2B2%280%2A0-2%2A%28-1%29%29=4