题目内容

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

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

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

设\[f(x) = \left| {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}&{{a_{13}}}&x\\ {{a_{21}}}&{{a_{22}}}&x&{{a_{24}}}\\ {{a_{31}}}&x&{{a_{33}}}&{{a_{34}}}\\ x&{{a_{42}}}&{{a_{43}}}&{{a_{44}}} \end{array}} \right|\],则多项式`\f(x)`中`\x^3`的系数为( )

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

设有行列式\[\left| {\begin{array}{*{20}{c}} x&2&3\\ { - 1}&x&0\\ 0&x&1 \end{array}} \right| = 0\],则`\x=`( )

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

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