Vector Spaces and Subspaces

Check if the set $H= \left\{\begin{bmatrix}3s\\2s\\3s-2\end{bmatrix}: s \in \mathbb{R}\right\}$ is a subspace of $\mathbb{R}^3$. Justify your answer.




Is the following set a subspace of $\mathbb{P}_2$. All polynomials of the form $p(t)=a+bt^2$, where $a, b\in \mathbb{R}$.




Determine if the set $H$ of all matrices of the form $\left[\begin{array}{ll}a & b \\ 0 & -a\end{array}\right]$ is a subspace of $M_{2 \times 2}$, the vector space of all $2\times 2$ matrices.

 

Soution of problems 1-3.