\begin{bmatrix}1 & h& h^2 & 1\\ h^2 & h & 1 & 2\\h & h^2 & 1 & 1 \end{bmatrix}
Given the matrix above is an augmented matrix, what is the possible value h where there is no solutions, unique solutions, and infinite solutions?
I have tried
1) reducing the matrix to \begin{bmatrix}1 & h& h^2 & 1\\ 0 & h-h^2 & 1-h^2 & 1-h^2 \\ 0 & 0 & 1-h^3 & 2-h \end{bmatrix}
2) For infinite soloution $$1-h^3 = 2-h$$ $$h^3-h+1 = 0$$
3) For no solution $$ 1-h^3 = 0$$ $$ h = 1$$ $$ h -2 = 0 $$ $$h = 2$$
4) For unique solution $$ h\neq 1,2$$
I am a bit unsure of whether my solution because it seems weird for my answer of infinite solutions.
