使用矩阵解方程组

使用矩阵解方程组
几何画板及绘图内容加载中,请稍等……
2015-05-15 02:05
本范例演示如何使用矩阵方法解线性方程组。核心数学概念包括矩阵运算和线性代数。通过构造摘要中的GeoGebra命令,可以观察到使用矩阵生成、求解和验证方程组的过程。适合高中数学课程中的代数与解析几何教学。

GeoGebra 命令及参数

  1. TableText({{x1 + "x" + y1t + "y=" + r1}, {x2 + "x" + y2t + "y=" + r2}}, "l{") → form1
  2. TableText({{"a", "b"}, {"m", "-n"}}, "c[]") → matGen
  3. TableText({{"x"}, {"y"}}, "c[]") → vecVars
  4. TableText({{"c"}, {"-p"}}, "c[]") → vecSolsGen
  5. TableText({{"ax+by=c"}, {"mx-ny=-p"}}, "l{") → form2
  6. TableText({{r1}, {r2}}, "c[]") → vecSols
  7. TableText({{x1, y1}, {x2, y2}}, "c[]") → matCoef
  8. TableText({{"d", "-b"}, {"-c", "a"}}, "c[]") → mat3
  9. TableText({{"a", "b"}, {"c", "d"}}, "c[]") → mat2
  10. TableText({{"(" + y2 + ")", "-(" + y1 + ")"}, {"-(" + x2 + ")", "(" + x1 + ")"}}, "c[]") → matb2
  11. TableText({{y2 + "(" + x1 + ")" + (If[(-y1) < 0, "", "+"]) + ((-y1)) + "(" + x2 + ")", y2 + "(" + y1 + ")" + (If[(-y1) < 0, "", "+"]) + ((-y1)) + "(" + y2 + ")"}, {x2 + "(" + x1 + ")" + (If[(-x1) < 0, "", "+"]) + ((-x1)) + "(" + x2 + ")", x2 + "(" + y1 + ")" + (If[(-x1) < 0, "", "+"]) + ((-x1)) + "(" + y2 + ")"}}, "c[]") → MatStep
  12. TableText({{y2 + "(" + r1 + ")" + (If[(-y1) < 0, "", "+"]) + ((-y1)) + "(" + r2 + ")"}, {x2 + "(" + r1 + ")" + (If[(-x1) < 0, "", "+"]) + ((-x1)) + "(" + r2 + ")"}}, "c[]") → vecSolsStep
  13. TableText({{"\frac{1}{" + det1 + "}•" + (x((det1 * Sol)))}, {"\frac{1}{" + det1 + "}•" + (y((det1 * Sol)))}}, "c[]") → vecSolInt
  14. TableText({{"\frac{1}{" + det1 + "}•" + det1, "\frac{1}{" + det1 + "}•0"}, {"\frac{1}{" + det1 + "}•0", "\frac{1}{" + det1 + "}•" + det1}}, "c[]") → matInt
  15. Textfield(x1) → inputBoxx1
  16. Textfield(y1) → inputBoxy1
  17. Textfield(r1) → inputBoxr1
  18. TableText({{"ax+by=c"}, {"mx+ny=+p"}}, "l{") → form3
  19. Textfield(x2) → inputBoxx2
  20. Textfield(y2) → inputBoxy2
  21. Textfield(r2) → inputBoxr2