Linear AlgebraUniversity
2×2 Matrix Determinant
det(A) = ad - bc
Calculate determinant of a 2×2 matrix [[a,b],[c,d]]
4 variablesSolve
Linear AlgebraUniversity
Dot Product of Vectors
a · b = a₁b₁ + a₂b₂ + a₃b₃
Calculate the dot product of two 3D vectors
6 variablesSolve
Linear AlgebraHigh School
Vector Magnitude
|v| = √(x² + y² + z²)
Calculate the length of a 3D vector
3 variablesSolve
Linear AlgebraUniversity
Eigenvalues of 2×2 Matrix
λ = (a+d ± √((a+d)²-4(ad-bc)))/2
Calculate eigenvalues of 2×2 matrix
4 variablesSolve
Linear AlgebraUniversity
2×2 Matrix Multiplication
[a b; c d] × [e f; g h] = [ae+bg af+bh; ce+dg cf+dh]
Multiply two 2×2 matrices
8 variablesSolve
Linear AlgebraUniversity
2×2 Matrix Inverse
A⁻¹ = (1/det) × [d -b; -c a], det = ad - bc
Find the inverse of a 2×2 matrix
4 variablesSolve
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Linear AlgebraUniversity
3×3 Matrix Determinant
det = a(ei - fh) - b(di - fg) + c(dh - eg)
Calculate the determinant of a 3×3 matrix
9 variablesSolve
Linear AlgebraUniversity
Cross Product of Vectors
a × b = (a₂b₃-a₃b₂, a₃b₁-a₁b₃, a₁b₂-a₂b₁)
Calculate the cross product of two 3D vectors and its magnitude
6 variablesSolve
