Question

Find the Wronskian of the following set of function
{1-x,1+x, 1-3x}

Answer 1

f₁=1-x

f₂=1+x

f₃=1-3x

$W=\begin{bmatrix} f_1 & f_2 & f_3 \\ f_1' & f_2' & f_3' \\ f_1'' & f_2'' & f_3'' \end{bmatrix}$

$W=\begin{bmatrix} 1-x & 1+x & 1-3x \\ -1 & 1 & -3 \\ 0 & 0 & 0 \end{bmatrix}$

=(1-x)$\begin{bmatrix} 1 & -3 \\ 0 & 0 \end{bmatrix}$ -(1+x)$\begin{bmatrix} -1 & -3 \\ 0 & 0 \end{bmatrix}$ +(1-3x)$\begin{bmatrix} -1 & 1 \\ 0 & 0 \end{bmatrix}$

=(1-x)(0-0)-(1-x)(0-0)+(1-3x)(0-0)

=0