Linear Algebra Subspace of Polynomial Question Help please

Looks like the other thread was deleted without my reply being restored.

You can write the equations in matrix form and show that it is linearly independent, by calculating to determinant of the matrix with constant coefficients.

How do I write the equations in matrix form?

$\begin{pmatrix} 1 & -1 & 0\\ 1 &0 &-1 \\ 0&1 & 0 \end{pmatrix} \begin{pmatrix} 1\\ t\\ t^2 \end{pmatrix}$

Start with writing the degrees of t as a column vector and then in the 3x3 matrix, write the coefficients of the equations along the rows.

$\begin{pmatrix} 1 & -1 & 0\\ 1 &0 &-1 \\ 0&1 & 0 \end{pmatrix} \begin{pmatrix} 1\\ t\\ t^2 \end{pmatrix}$

Start with writing the degrees of t as a column vector and then in the 3x3 matrix, write the coefficients of the equations along the rows.

Any hints on this question would be greatly appreciated

Looks like the other thread was deleted without my reply being restored.

You can write the equations in matrix form and show that it is linearly independent, by calculating to determinant of the matrix with constant coefficients.