Viết ma trận của dạng toàn phương Q trong cơ sở chính tắc: \[Q({x_1},{x_2},{x_3}) = 3{x_1}^2 + 2{x_2}^2 - {x_3}^2 + 2{x_1}{x_2} - 4{x_1}{x_3} + 2{x_2}{x_3}\]

A. p = 1, q = 2

B. p = 2, q = 1

C. p = 1, q = 1

D. p = 0, q = 2

A. \[A = \left( {\begin{array}{*{20}{c}}{\frac{1}{{\sqrt 3 }}}&0&{\frac{2}{{\sqrt 6 }}}\\{\frac{1}{{\sqrt 3 }}}&{\frac{1}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 6 }}}\\2&{ - 1}&3\end{array}} \right),{P^{ - 1}}AP = \left( {\begin{array}{*{20}{c}}3&0&0\\0&5&0\\0&0&9\end{array}} \right)\]

B. \[A = \left( {\begin{array}{*{20}{c}}{\frac{{ - 2}}{{\sqrt 6 }}}&0&{\frac{1}{{\sqrt 3 }}}\\{\frac{1}{{\sqrt 6 }}}&{\frac{1}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 3 }}}\\{\frac{{ - 1}}{{\sqrt 6 }}}&{\frac{{ - 1}}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 3 }}}\end{array}} \right),{P^{ - 1}}AP = \left( {\begin{array}{*{20}{c}}{ - 2}&0&0\\0&4&0\\0&0&4\end{array}} \right)\]

A. \[I = \frac{2}{3}x\sqrt x + 2\sqrt x + C\]

B. \[I = \frac{1}{3}x\sqrt x + 2\sqrt x + C\]

C. \[I = \frac{2}{3}x\sqrt x + 3\sqrt x + C\]

D. \[I = \frac{2}{3}{x^2}\sqrt x + 3\sqrt x + C\]

A. p=1,q=3p=1,q=3

B. p=3,q=1p=3,q=1

C. p=2,q=2p=2,q=2

D. p=1,q=2p=1,q=2

A. \[\left( {\begin{array}{*{20}{c}}\begin{array}{l}2\\ - 3\end{array}&\begin{array}{l} - 3\\1\end{array}\end{array}} \right)\]

B. \[\left( {\begin{array}{*{20}{c}}\begin{array}{l}2\\ - 1\end{array}&\begin{array}{l} - 1\\ - 3\end{array}\end{array}} \right)\]

C. \[\left( {\begin{array}{*{20}{c}}\begin{array}{l}2\\ - 6\end{array}&\begin{array}{l} - 6\\1\end{array}\end{array}} \right)\]

D. \[\left( {\begin{array}{*{20}{c}}\begin{array}{l}2\\0\end{array}&\begin{array}{l} - 6\\1\end{array}\end{array}} \right)\]

A. \[I = 60\frac{2}{7}\]

B. \[I = 66\frac{2}{7}\]

C. \[I = - 60\frac{2}{7}\]

D. \[I = - 66\frac{2}{7}\]