🔬 Singularity & Dimension Sandbox
Test custom 3×3 coefficient matrices to verify if they represent a singular or non-singular system. Compare your results with the cases outlined in Lecture 1.
Load Preset Systems:
Case I: Equations provide distinct information. They cross at exactly one point. Determinant is non-zero, and the matrix is invertible.
Coefficient Matrix [A] (3×3)
a11
a12
a13
a21
a22
a23
a31
a32
a33
Mathematical Diagnostics
DETERMINANT:
det(A) = 1
SINGULARITY STATE:
NON-SINGULAR (det ≠ 0)Geometric Outlay: The equations describe independent spans that meet at a unique coordinate. This system is fully solvable and the matrix is invertible.
Equivalent System of Equations (Mock Target: y = [0, 0, 0]ᵀ)
1x₁ + 1x₂ + 1x₃ = 0
1x₁ + 2x₂ + 1x₃ = 0
1x₁ + 1x₂ + 2x₃ = 0