find k give that
|1 k 3 |
|k 1 -1| = 7
|3 4 2 |
btw.. this is suposed to be a matix

Question

find k give that 
|1    k    3  |
|k    1    -1|    = 7 
|3    4    2  |
btw.. this is suposed to be a matix

anonymous · Answer

woops matrix

anonymous · Answer

it is clear what you have to do right?  take the determinant and set it equal to 7, solve for k

anonymous · Answer

that is, solve 
$$-2 k^2+9 k-3=7$$ a quadratic equation

anonymous · Answer

yahh but like my result doesnt make any sence

anonymous · Answer

yas i got that equation.. but like my result does make sence

jamesj · Answer

Why not?  What values of k did you find?

anonymous · Answer

like 1.113406013 and then -5.6134

anonymous · Answer

that makes no sence of me ha

jamesj · Answer

no, that's right.  
$$ 2k^2 - 9k  + 10 = 0 $$  Now use the quadratic formula.

anonymous · Answer

its right? yah i used that one

anonymous · Answer

i checked in the answer booklet it says like 2 or 5/2

anonymous · Answer

Yes, after applying Laplace expansion to that matrix you will get a quadratic equation equation which will be $ 2k^2 - 9k  + 10 = 0 $ and now if you solve for k then you will get k=2 or $K = \frac 5 2 $.

anonymous · Answer

now how do you get that though?

anonymous · Answer

Factor $$ 2k^2 - 9k  + 10 = 0 $$

jamesj · Answer

c'mon.  In standard notation 
a = 2, b = -9, c = 10.  

Hence 
$$ b^2 - 4ac = 81 - 80 = 1 $$

and therefore the roots
$$ k = \frac{ -b \pm \sqrt{b^2-4ac}}{2a} = \frac{9 \pm 1}{4} = 2 \ or \ 5/2 $$

anonymous · Answer

`thank you!!!