题目内容
设` \alpha,\beta `为` R^n `中两个非零正交列向量 ，` A=\alpha\beta^T `，则` A `（ ）
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设\[D = \left| {\begin{array}{*{20}{c}} 1&2&3&4\\ 2&3&4&1\\ 3&4&1&2\\ 4&1&2&3 \end{array}} \right| = \Delta ({a_{{\rm{ij}}}})\]，`\A_{ij}`表示元素`\a_{ij}`的代数余子式，则`\A_{14} + 2A_{24} + 3A_{34} + 4A_{44} = ` （ ）
设n阶行列式`\D = a \ne 0`，且D中的每列的元素之和为b，则行列式D中的第二行的代数余子式之和为（ ）
如\[\left| {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}&{{a_{13}}}\\ {{a_{21}}}&{{a_{22}}}&{{a_{23}}}\\ {{a_{31}}}&{{a_{32}}}&{{a_{33}}} \end{array}} \right| = 2\]，则\[\left| {\begin{array}{*{20}{c}} {2{a_{11}}}&{2{a_{12}}}&{2{a_{12}} - 2{a_{13}}}\\ {2{a_{21}}}&{2{a_{22}}}&{2{a_{22}} - 2{a_{23}}}\\ {2{a_{31}}}&{2{a_{32}}}&{2{a_{32}} - 2{a_{33}}} \end{array}} \right| = ,\left| {\begin{array}{*{20}{c}} {2{a_{11}}}&{{a_{21}} - 3{a_{11}}}&{{a_{21}} - {a_{31}}}\\ {2{a_{12}}}&{{a_{22}} - 3{a_{12}}}&{{a_{22}} - {a_{32}}}\\ {2{a_{13}}}&{{a_{23}} - 3{a_{13}}}&{{a_{23}} - {a_{33}}} \end{array}} \right| = ,\left| {\begin{array}{*{20}{c}} 0&0&0&2\\ {{a_{11}}}&{{a_{21}}}&{{a_{31}}}&1\\ {{a_{12}}}&{{a_{22}}}&{{a_{32}}}&2\\ {{a_{13}}}&{{a_{23}}}&{{a_{33}}}&3 \end{array}} \right| = \]分别等于（ ）
如果\[\left| {\begin{array}{*{20}{c}} a&3&1\\ b&0&1\\ c&2&1 \end{array}} \right| = 1\]，则\[\left| {\begin{array}{*{20}{c}} {a - 3}&{b - 3}&{c - 3}\\ 5&2&4\\ 1&1&1 \end{array}} \right| = \]（ ）
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