The fuction D(t) is the determinant of a 4x4 matrix:

D(t) = |1 2 3 4|

|-1 0 -2 0|

|4 3 2 1|

|1 1 2 t|

Find the determinant D(t) and find the value t0 which gives D(t0) = 2/7

Thanks!

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- Feb 17th 2010, 04:32 PMgralla55Determinant problem
The fuction D(t) is the determinant of a 4x4 matrix:

D(t) = |1 2 3 4|

|-1 0 -2 0|

|4 3 2 1|

|1 1 2 t|

Find the determinant D(t) and find the value t0 which gives D(t0) = 2/7

Thanks! - Feb 17th 2010, 06:52 PMtonio
- Feb 17th 2010, 08:32 PMRoam
You could use the Laplace expansion, If you are confused about the method to be used for evaluating det of this 4x4 matix. Firstly, you choose any element $\displaystyle a_{ij}=1$ or, if lacking, $\displaystyle a_{ij} \neq 0 $. Then you use $\displaystyle a_{ij}$ as a pivot, apply elementary row [column] operations to put 0s in all other positions in column j [row i]. Then expand the determinant cofactors of column j [row i]. Let's see how you go.

- Feb 18th 2010, 06:51 AMgralla55
Ok thanks, I got the determinant to be 25. Still, how do I find the value t0 which gives D(t0) = 2/7 ?

- Feb 18th 2010, 12:38 PMgralla55
Isn't there any program which solves this type of problem? I just need the answer for a t0 which gives D(t0) = 2/7, no explanation needed :P

- Feb 18th 2010, 12:43 PMicemanfan
- Feb 18th 2010, 12:47 PMgralla55
"What you need is a way to write D(t) as a polynomial function of t."

Just realized that! But how? I have 1 hour to solve this, and I don't have my books here so I kinda need some help :P Would very much appreciate it! - Feb 18th 2010, 01:03 PMicemanfan
Just find the formula for calculating determinants of 4x4 matrices and apply it.

- Feb 18th 2010, 01:46 PMgralla55
Sure, but I don't have my books and that's why I'm asking :P Anyone? I have very little time left =( (10 hours)