线性方程组\(\left\{ \matrix{ {x_1} + {x_2} + 2{x_3} - {x_4} = 0, \cr 2{x_1} + {x_2} + {x_3} - {x_4} = 0, \cr 2{x_1} + 2{x_2} + {x_3} + 2{x_4} = 0; \cr} \right.\)有无穷多解.
举一反三
- 曲线\( \left\{ {\matrix{ { { x^2} + {y^2} = {z^2}} \cr { { z^2} = y} \cr } } \right. \)在坐标面\( yoz \) 上的投影曲线方程为（ ） A: \( \left\{ {\matrix{ { { x^2} + { { \left( {y - {1 \over 2}} \right)}^2} = {1 \over 4}} \cr {z = 0} \cr } } \right. \) B: \( \left\{ {\matrix{ { { z^2} = y} \cr {x = 0} \cr } } \right. \) C: \( \left\{ {\matrix{ {z = {y^2}} \cr {x = 0} \cr } } \right. \) D: \( \left\{ {\matrix{ { { y^2} + { { \left( {x - {1 \over 2}} \right)}^2} = {1 \over 4}} \cr {z = 0} \cr } } \right. \)
- 设方程组\[\left\{ {\begin{array}{*{20}{c}} {\lambda {x_1} + {x_2} + {x_3} = \lambda - 3}\\ {{x_1} + \lambda {x_2} + {x_3} = - 2}\\ {{x_1} + {x_2} + \lambda {x_3} = - 2} \end{array}} \right.\]若`\lambda = 1`，则( )
- 在其定义区间上连续的函数是( )。 A: \(f(x) = \left\{ {\matrix{ {x\quad ,{\rm{0}} \le x \le {\rm{1}}} \cr {1 - x\quad ,1 < x \le 2} \cr } } \right.\) B: \(f(x) = \left\{ {\matrix{ {x\quad ,0 < x \le 1 } \cr {2 - x\quad ,1 < x \le 2} \cr } } \right.\) C: \(f(x) = \left\{ {\matrix{ {x\;\quad ,0 \le x < 1} \cr {0\;\quad \quad ,x = 1} \cr {2 - x\quad ,1 < x \le 2} \cr } } \right.\) D: \(f(x) = \left\{ {\matrix{ { { 1 \over {x - 1}}\quad ,0 \le x \le 1} \cr {0\quad ,1 \le x \le 2} \cr } } \right.\)
- 下列函数中，( )是初等函数. A: \(y = \arcsin ({x^2} + 2)\) B: \(f(x) = \left\{ \matrix{ 0,x \notin Q \ \cr 1,x \in Q \ \cr} \right.\) C: \(y = \sqrt { - {x^2} + 1} \) D: \(f(x) = \left\{ \matrix{ {x^2},0 \le x < 1 \ \cr x + 1,x > 1 \ \cr} \right.\)
- 函数\(f(x) = \left\{ {\matrix{ { { x^2} - 1\;, - 1 \le x < 0} \cr {x\;\quad \;,0 \le x < 1} \cr {2 - x\;\quad ,1 \le x \le 2} \cr } } \right.\)在\(x =\)（ ）处间断。______