Mathematics II2080.15 marksVector spaces and subspaces
Show that H = (a-3b, b-a, a, b) : a, b in mathbbR is a subspace of mathbbR4.
Show that $H = {(a-3b, b-a, a, b) : a, b \in \mathbb{R}}$ is a subspace of $\mathbb{R}^4$. [5]
Given: $$H = {(a-3b,\ b-a,\ a,\ b) : a, b \in \mathbb{R}}$$ We rewrite a general element of H by separating the parameters $a$ and $b$: $$\begin{pmatrix} a-3b \ b-a \ a \ b \end{pmatrix} = a\begin{pmatrix} 1 \ -1 \ 1 \ 0 \end{pmatrix} + b\begin{pmatrix} -3 \ 1 \ 0 \ 1 \end{pmatrix}$$ D...