Exercise 4.1.9

Answers

Directly check that

\det ((\begin{matrix} a & b \\ c & d \end{matrix}) (\begin{matrix} e & f \\ g & h \end{matrix})) = \det (\begin{matrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{matrix})

= (ae + bg) (cf + dh) - (af + bh) (ce + dg) = ad (eh - fg) - bc (eh - fg) = (ad - bc) (eh - fg)

= \det (\begin{matrix} a & b \\ c & d \end{matrix}) \times \det (\begin{matrix} e & f \\ g & h \end{matrix}) .

jephianlin

2011-06-27 00:00