2021年高考数学上海春6 |
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2022-05-03 08:24:23 |
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6.(4分)若方程组$\left\{\begin{array}{l}{{a}_{1}x+{b}_{1}y={c}_{1}}\\ {{a}_{2}x+{b}_{2}y={c}_{2}}\end{array}\right.$无解,则$\left\vert \begin{array}{l}{{a}_{1}}&{{b}_{1}}\\ {{a}_{2}}&{{b}_{2}}\end{array}\right\vert =$____. 分析:利用二元一次方程组的解的行列式表示进行分析即可得到答案. 解:对于方程组$\left\{\begin{array}{l}{{a}_{1}x+{b}_{1}y={c}_{1}}\\ {{a}_{2}x+{b}_{2}y={c}_{2}}\end{array}\right.$,有$D=\left\vert \begin{array}{l}{{a}_{1}}&{{b}_{1}}\\ {{a}_{2}}&{{b}_{2}}\end{array}\right\vert ,{D}_{x}=\left\vert \begin{array}{l}{{c}_{1}}&{{b}_{1}}\\ {{c}_{2}}&{{b}_{2}}\end{array}\right\vert ,{D}_{y}=\left\vert \begin{array}{l}{{a}_{1}}&{{c}_{1}}\\ {{a}_{2}}&{{c}_{2}}\end{array}\right\vert$, 根据题意,方程组$\left\{\begin{array}{l}{{a}_{1}x+{b}_{1}y={c}_{1}}\\ {{a}_{2}x+{b}_{2}y={c}_{2}}\end{array}\right.$无解, 所以$D=0$,即$D=\left\vert \begin{array}{l}{{a}_{1}}&{{b}_{1}}\\ {{a}_{2}}&{{b}_{2}}\end{array}\right\vert =0$, 故答案为:0. 点评:本题考查的是二元一次方程组的解行列式表示法,这种方法可以使得方程组的解与对应系数之间的关系表示的更为清晰,解题的关键是熟练掌握二元一次方程组的解行列式表示法中对应的公式.
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