SOLUTION: Show without expanding that x = 2 is a root of the equation | x -6 -1 | | 2 -3x x - 3| ==0 and solve it completely. |-3 2x x + 2|

Algebra ->  Matrices-and-determiminant -> SOLUTION: Show without expanding that x = 2 is a root of the equation | x -6 -1 | | 2 -3x x - 3| ==0 and solve it completely. |-3 2x x + 2|       Log On


   

Question 969027: Show without expanding that x = 2 is a root of the equation
| x -6 -1 |
| 2 -3x x - 3| ==0 and solve it completely.
|-3 2x x + 2|
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Show without expanding that x = 2 is a root of the equation
%22%22=%22%22%220%22 and solve it completely.

Substitute x=2 in the determinant

%22%22=%22%22%220%22
 

abs%28matrix%283%2C3%2C%0D%0A+2%2C-6%2C-1%2C%0D%0A2%2C-6%2C-1%2C++%0D%0A-3%2C4%2C4%29%29%22%22=%22%22%220%22

The first two rows are the same, so if you subtract
the second row from the top row you get

abs%28matrix%283%2C3%2C%0D%0A+0%2C0%2C0%2C%0D%0A2%2C-6%2C-1%2C++%0D%0A-3%2C4%2C4%29%29%22%22=%22%22%220%22

If this were expanded about the top row, all the minors
would be multiplied by 0 giving 0.

Edwin