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 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.