使用矩阵解方程组
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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
TableText({{x1 + "x" + y1t + "y=" + r1}, {x2 + "x" + y2t + "y=" + r2}}, "l{") → form1TableText({{"a", "b"}, {"m", "-n"}}, "c[]") → matGenTableText({{"x"}, {"y"}}, "c[]") → vecVarsTableText({{"c"}, {"-p"}}, "c[]") → vecSolsGenTableText({{"ax+by=c"}, {"mx-ny=-p"}}, "l{") → form2TableText({{r1}, {r2}}, "c[]") → vecSolsTableText({{x1, y1}, {x2, y2}}, "c[]") → matCoefTableText({{"d", "-b"}, {"-c", "a"}}, "c[]") → mat3TableText({{"a", "b"}, {"c", "d"}}, "c[]") → mat2TableText({{"(" + y2 + ")", "-(" + y1 + ")"}, {"-(" + x2 + ")", "(" + x1 + ")"}}, "c[]") → matb2TableText({{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[]") → MatStepTableText({{y2 + "(" + r1 + ")" + (If[(-y1) < 0, "", "+"]) + ((-y1)) + "(" + r2 + ")"}, {x2 + "(" + r1 + ")" + (If[(-x1) < 0, "", "+"]) + ((-x1)) + "(" + r2 + ")"}}, "c[]") → vecSolsStepTableText({{"\frac{1}{" + det1 + "}•" + (x((det1 * Sol)))}, {"\frac{1}{" + det1 + "}•" + (y((det1 * Sol)))}}, "c[]") → vecSolIntTableText({{"\frac{1}{" + det1 + "}•" + det1, "\frac{1}{" + det1 + "}•0"}, {"\frac{1}{" + det1 + "}•0", "\frac{1}{" + det1 + "}•" + det1}}, "c[]") → matIntTextfield(x1) → inputBoxx1Textfield(y1) → inputBoxy1Textfield(r1) → inputBoxr1TableText({{"ax+by=c"}, {"mx+ny=+p"}}, "l{") → form3Textfield(x2) → inputBoxx2Textfield(y2) → inputBoxy2Textfield(r2) → inputBoxr2