1

Suppose T e L(F" Fm ) . Show that there exist scalars Ajk e F for J = m and k such thatT(1. ~n) (AL++ALnSn.Am.11 + +Am nSn)for every Ga Xn) e F" [The exer...

Question

Suppose T e L(F" Fm ) . Show that there exist scalars Ajk e F for J = m and k such thatT(1. ~n) (AL++ALnSn.Am.11 + +Am nSn)for every Ga Xn) e F" [The exercise above shows that T has the form promised in the last item of Example 3.4.1

Suppose T e L(F" Fm ) . Show that there exist scalars Ajk e F for J = m and k such that T(1. ~n) (AL++ALnSn. Am.11 + +Am nSn) for every Ga Xn) e F" [The exercise above shows that T has the form promised in the last item of Example 3.4.1



Answers

In Exercises $33-36,$ verify that det $E A=(\operatorname{det} E)(\operatorname{det} A),$ where $E$ is the elementary matrix shown and $A=\left[\begin{array}{cc}{a} & {b} \\ {c} & {d}\end{array}\right]$
$$
\left[\begin{array}{ll}{1} & {0} \\ {0} & {k}\end{array}\right]
$$


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