Exercise 13

Assume that $B=\langle\vec{\beta}_{1},\vec{\beta}_{2},\vec{\beta}_{3},\vec{\beta}_{4}\rangle$ is a basis for a vector space. Represent with respect to $B,B$ the transformation that is determined by each.

• $\vec{\beta}_{1}\mapsto\vec{\beta}_{2}$, $\vec{\beta}_{2}\mapsto\vec{\beta}_{3}$, $\vec{\beta}_{3}\mapsto\vec{\beta}_{4}$, $\vec{\beta}_{4}\mapsto\vec{0}$

• $\vec{\beta}_{1}\mapsto\vec{\beta}_{2}$, $\vec{\beta}_{2}\mapsto\vec{0}$, $\vec{\beta}_{3}\mapsto\vec{\beta}_{4}$, $\vec{\beta}_{4}\mapsto\vec{0}$

• $\vec{\beta}_{1}\mapsto\vec{\beta}_{2}$, $\vec{\beta}_{2}\mapsto\vec{\beta}_{3}$, $\vec{\beta}_{3}\mapsto\vec{0}$, $\vec{\beta}_{4}\mapsto\vec{0}$