# Determinant problem

• Feb 17th 2010, 05:32 PM
gralla55
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!
• Feb 17th 2010, 07:52 PM
tonio
Quote:

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
• Feb 17th 2010, 09:32 PM
Roam
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.
• Feb 18th 2010, 07:51 AM
gralla55
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, 01:38 PM
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
• Feb 18th 2010, 01:43 PM
icemanfan
Quote:

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.
• Feb 18th 2010, 01:47 PM
gralla55
"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, 02:03 PM
icemanfan
Just find the formula for calculating determinants of 4x4 matrices and apply it.
• Feb 18th 2010, 02:46 PM
gralla55
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)