ข้อสอบ PAT 1 - ตุลาคม 2555

$$\begin{gathered} \underline{\mathrm{ข้อ} \left(\mathrm{ก}\right)} \\ \mathrm{จากโจทย์} {\left[\det \left(\mathrm{A}\right)\right]}^3=\det \left[\mathrm{adj}\left(\mathrm{A}\right) \right] \\ ={\left[\det \left(\mathrm{A}\right)\right]}^{\mathrm{n}-1} ; \mathrm{มิติ} 3\times 3 \\ ={\left[\det \left(\mathrm{A}\right)\right]}^{3-1} \\ ={\left[\det \left(\mathrm{A}\right)\right]}^2 \mathrm{ข้อ} \mathrm{ก} \mathrm{ผิด} \\ \underline{\mathrm{ข้อ} \left(ข\right)} \\ \mathrm{จากโจทย์} {\mathrm{A}}^2=2\mathrm{A} \\ \det \left({\mathrm{A}}^2\right)=\det \left(2\mathrm{A}\right) \\ {\left(\det \mathrm{A}\right)}^2=2^{\mathrm{n}} \det \mathrm{A} \\ {\left(\det \mathrm{A}\right)}^2=2^3 \det \mathrm{A} ; \mathrm{โดย} \det \mathrm{A}\ne 0 \\ \det \mathrm{A}=2^3 \\ \det \mathrm{A}=8 \mathrm{ข้อ} \mathrm{ข} \mathrm{ผิด} \end{gathered}$$