Question

Need help with this linear algebra problem

Answer 1

You should have

$L(t)=\begin{bmatrix}1\\1\end{bmatrix}+t\begin{bmatrix}2\\-3\end{bmatrix}$

$\mathbf v$ on its own points to the point (2, -3) and lies on the line through this point and the origin. We capture all points on this line by scaling $\mathbf v$ by $t$. Then we add to $t\mathbf v$ another vector that points to P(1, 1), which shifts the endpoint of all vectors on the line $t\mathbf v$ to the line through P that runs parallel to $t\mathbf v$.