User:A2569875/模板沙盒/數學測試/3

• ${{\begin{bmatrix}{\cos \left({{45}\,{{}^{\circ }}}\right)}&{-{\sin \left({{45}\,{{}^{\circ }}}\right)}}\\{\sin \left({{45}\,{{}^{\circ }}}\right)}&{\cos \left({{45}\,{{}^{\circ }}}\right)}\end{bmatrix}}\times {vector\left({\frac {1}{\sqrt {2}}},\,{\frac {1}{\sqrt {2}}}\right)}}={\begin{bmatrix}{0}\\{1}\end{bmatrix}}$
• ${{\begin{bmatrix}{\cos \left({{45}\,{{}^{\circ }}}\right)}&{-{\sin \left({{45}\,{{}^{\circ }}}\right)}}\\{\sin \left({{45}\,{{}^{\circ }}}\right)}&{\cos \left({{45}\,{{}^{\circ }}}\right)}\end{bmatrix}}\,{\begin{bmatrix}1\\0\end{bmatrix}}}={\begin{bmatrix}{0.70710678118655}\\{0.70710678118655}\end{bmatrix}}$
• ${{\begin{bmatrix}{\cos \left({{60}\,{{}^{\circ }}}\right)}&{-{\sin \left({{60}\,{{}^{\circ }}}\right)}}\\{\sin \left({{60}\,{{}^{\circ }}}\right)}&{\cos \left({{60}\,{{}^{\circ }}}\right)}\end{bmatrix}}\,{\begin{bmatrix}{\frac {\sqrt {3}}{2}}\\{\frac {1}{2}}\end{bmatrix}}}={\begin{bmatrix}{0}\\{1}\end{bmatrix}}$

---

• $\operatorname {round} \left(\log _{2}{\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,3\right)={\begin{bmatrix}{0.398+3.532i}&{1.483+1.53i}&{-0.074-2.166i}\\{1.409-0.637i}&{0.52-0.276i}&{2.286+0.39i}\\{1.36-2.081i}&{2.663-0.901i}&{1.667+1.276i}\end{bmatrix}}$
• $\operatorname {round} \left({{2}^{\log _{2}{\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}}},\,3\right)={\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}$
• $\operatorname {round} \left(\ln {\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,3\right)={\begin{bmatrix}{0.276+2.448i}&{1.028+1.06i}&{-0.051-1.501i}\\{0.977-0.441i}&{0.361-0.191i}&{1.585+0.271i}\\{0.943-1.442i}&{1.846-0.625i}&{1.156+0.885i}\end{bmatrix}}$
• $\operatorname {round} \left(e^{\ln {\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}$

• $\operatorname {round} \left(\ln {\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}},\,3\right)={\begin{bmatrix}{-0.534+2.652i}&{0.722-0.721i}\\{1.806-1.802i}&{1.633+0.49i}\end{bmatrix}}$
• $\operatorname {round} \left(e^{\ln {\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}$
• $\operatorname {round} \left(e^{{\ln {\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}}\times {\begin{bmatrix}{3}&{6}\\{7}&{9}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{111880867330.3+289269930190.11i}&{160816129651.98+418718548369.82i}\\{753700363714.63-111717403084.54i}&{1090370340897.3-158999398148.36i}\end{bmatrix}}$

• $\operatorname {round} \left({{\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}^{\begin{bmatrix}{3}&{0}\\{0}&{3}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{91}&{134}\\{335}&{493}\end{bmatrix}}$
• $\operatorname {round} \left(\log _{\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}\left({{\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}^{\begin{bmatrix}{3}&{0}\\{0}&{3}\end{bmatrix}}}\right),\,3\right)={\begin{bmatrix}{1.474+0.498i}&{0.415-0.135i}\\{1.037-0.338i}&{2.718+0.092i}\end{bmatrix}}$

• $\operatorname {round} \left({{\begin{bmatrix}{2}&{0}\\{0}&{2}\end{bmatrix}}^{\begin{bmatrix}{3}&{0}\\{0}&{3}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{8}&{0}\\{0}&{8}\end{bmatrix}}$
• $\operatorname {round} \left(\log _{\begin{bmatrix}{2}&{0}\\{0}&{2}\end{bmatrix}}\left({{\begin{bmatrix}{2}&{0}\\{0}&{2}\end{bmatrix}}^{\begin{bmatrix}{3}&{0}\\{0}&{3}\end{bmatrix}}}\right),\,3\right)={\begin{bmatrix}{3}&{0}\\{0}&{3}\end{bmatrix}}$

• $\operatorname {round} \left({{\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}^{\begin{bmatrix}{3}&{6}\\{7}&{9}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{111880867330.23+289269930190.14i}&{160816129651.89+418718548369.86i}\\{753700363714.65-111717403084.35i}&{1090370340897.3-158999398148.09i}\end{bmatrix}}$
• $\operatorname {round} \left(\log _{\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}\left({{\begin{bmatrix}{1}&{2}\\{5}&{7}\end{bmatrix}}^{\begin{bmatrix}{3}&{6}\\{7}&{9}\end{bmatrix}}}\right),\,3\right)={\begin{bmatrix}{2.384+2.358i}&{2.506+4.378i}\\{7.237-1.673i}&{11.409-2.956i}\end{bmatrix}}$