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二十、矩阵\(\begin{pmatrix}1&1&1\\2&3&0\\2&1&1\end{pmatrix}\)的QR分解为____。A. \(\begin{pmatrix} \frac{1}{3}&0&-\frac{4}{3\sqrt2}\\ \frac{2}{3}&\frac{1}{\sqrt2}&\frac{1}{3\sqrt2}\\ \frac{2}{3}&-\frac{1}{\sqrt2}&\frac{1}{3\sqrt2} \end{pmatrix} \begin{pmatrix} 3&3&1\\ 0&\sqrt2&-\frac{1}{\sqrt2}\\ 0&0&\frac{1}{\sqrt2} \end{pmatrix}\) B. \(\begin{pmatrix} \frac{1}{3}&0&\frac{4}{3\sqrt2}\\ \frac{2}{3}&\frac{1}{\sqrt2}&-\frac{1}{3\sqrt2}\\ \frac{2}{3}&-\frac{1}{\sqrt2}&-\frac{1}{3\sqrt2} \end{pmatrix} \begin{pmatrix} 3&3&1\\ 0&\sqrt2&-\frac{1}{\sqrt2}\\ 0&0&\frac{1}{\sqrt2} \end{pmatrix}\) C. \(\begin{pmatrix} 1&0&\frac{2}{3}\\ 2&1&-\frac{1}{6}\\ 2&-1&-\frac{1}{6} \end{pmatrix} \begin{pmatrix} 1&1&\frac{1}{3}\\ 0&1&-\frac{1}{2}\\ 0&0&1 \end{pmatrix}\) D. \(\begin{pmatrix} \frac{1}{3}&0&\frac{4}{3\sqrt2}\\ \frac{2}{3}&-\frac{1}{\sqrt2}&-\frac{1}{3\sqrt2}\\ \frac{2}{3}&\frac{1}{\sqrt2}&-\frac{1}{3\sqrt2} \end{pmatrix} \begin{pmatrix} 3&3&1\\ 0&\sqrt2&-\frac{1}{\sqrt2}\\ 0&0&\frac{1}{\sqrt2} \end{pmatrix}\)

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十九、设矩阵\(A=\begin{pmatrix}1&2&3\\-1&4&-3\\1&a&5\end{pmatrix}\)的特征方程有一个二重根，则以下断言正确的是____。A. \(A\)必可对角化 B. \(A\)必不可对角化 C. 不能确定

十八、实数域上全体\(n\)阶对称矩阵所构成的向量空间的维数是____。A. \(n\) B. \(\frac{n}{2}\) C. \(\frac{n(n-1)}{2}\) D. \(\frac{n(n+1)}{2}\)

十七、下列哪一矩阵\(A\)满足\(A^k\rightarrow 0\)当\(k\rightarrow\infty\)时。A. \(\begin{pmatrix}\frac{2}{3}&-\frac{2}{3}\\ \frac{4}{3}&\frac{2}{3}\end{pmatrix}\) B. \(\begin{pmatrix}\frac{1}{2}&\frac{1}{2}\\ \frac{1}{2}&\frac{1}{2}\end{pmatrix}\) C. \(\begin{pmatrix}2&-\frac{10}{3}\\ \frac{2}{3}&-1\end{pmatrix}\) D. \(\begin{pmatrix}0.8&0.3\\0.2&0.7\end{pmatrix}\)

十六、以\((-2,1,1),(-1,-1,2),(-1,-2,1),(1,2,2)\)为顶点的四面体的体积是____。A. \(\frac{3}{2}\) B. \(16\) C. \(9\) D. \(\frac{8}{3}\)