题目内容

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（）

A. \[\frac{a}{{{b^2}}}\]
B. \[\frac{{{a^2}}}{b}\]
C. \[\frac{{{a^2}}}{{{b^2}}}\]
D. \[\frac{a}{b}\]

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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（）

A. 16，4，4
B. -16，-4，-4
C. 16，-4，-4
D. -16，4，4

如果\[\left| {\begin{array}{{20}{c}} a&3&1\\ b&0&1\\ c&2&1 \end{array}} \right| = 1\]，则\[\left| {\begin{array}{{20}{c}} {a - 3}&{b - 3}&{c - 3}\\ 5&2&4\\ 1&1&1 \end{array}} \right| = \]（）

A. 0
B. -1
C. 1
D. -2

\[\left| {\begin{array}{*{20}{c}} 0&0&0&a\\ b&0&0&0\\ 0&c&0&0\\ 0&0&d&0 \end{array}} \right| = \]（）

A. `\abcd`
B. `\-abcd`
C. 0
D. `\abc`

如果\[\left| {\begin{array}{*{20}{c}} 1&2&3&4\\ 6&5&4&3\\ 0&0&2&x\\ 0&0&3&3 \end{array}} \right| = 0\]，则`\x=`（）

A. 0
B. 1
C. -1
D. 2