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Solve a System of Equations Using Matrices

Solve a System of Equations Using Matrices
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2015-05-15 02:05
VectorCoordinate GeometryMatrix
This example demonstrates solving a system of linear equations using matrix methods. Key mathematical concepts include matrix operations and linear algebra. The GeoGebra commands in the construction summary show the process of generating, solving, and verifying the system of equations. Suitable for high school algebra and coordinate geometry courses.

GeoGebra Commands & Parameters

  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