91Ó°ÊÓ

Suppose that \(C D=-D C\), and find the flaw in the following argument: Taking determinants gives \((\operatorname{det} C)(\operatorname{det} D)=-(\operatorname{det} D)(\operatorname{det} C)\), so either \(\operatorname{det} C=0\) or det \(D=0\). Thus \(C D=-D C\) is only possible if \(C\) or \(D\) is singular.

(a) Find the area of the parallelogram with edges \(v=(3,2)\) and \(w=(1,4)\). (b) Find the area of the triangle with sides \(v, w\), and \(v+w\). Draw it. (c) Find the area of the triangle with sides \(v, w\), and \(w-v\). Draw it.