# Math Help - Determinant problem

1. ## Determinant 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!

2. Originally Posted by gralla55
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!
You must know what to do to evaluate determinants of this kind if you were given this question to solve, so : what have you done so far and where are you stuck?

Tonio

3. 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 $a_{ij}=1$ or, if lacking, $a_{ij} \neq 0$. Then you use $a_{ij}$ 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.

4. Ok thanks, I got the determinant to be 25. Still, how do I find the value t0 which gives D(t0) = 2/7 ?

5. 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

6. Originally Posted by gralla55
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
What you need is a way to write D(t) as a polynomial function of t.

7. "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!

8. Just find the formula for calculating determinants of 4x4 matrices and apply it.

9. 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)