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Both calculators run independently — change the inputs on either side to compare results.

Quadratic Form Calculator

Evaluate a quadratic form Q(x) = x^T A x for a symmetric 2×2 matrix and a vector (x₁, x₂). Use it to test whether a matrix is positive definite, negative definite, or indefinite.

Matrix element (1,1)

Matrix element (1,2)

Matrix element (2,2)

Variable x₁

Variable x₂

Fill in the required fields to see your result.

Linear Algebra

2x2 Linear System Solver

Solve a system of two linear equations (ax + by = e and cx + dy = f) instantly. Use it when you need exact values of x and y that satisfy both equations simultaneously.

a (ax + by = e)

c (cx + dy = f)

Fill in the required fields to see your result.

Key differences

	Quadratic Form Calculator	2x2 Linear System Solver
Category	Linear Algebra	Linear Algebra
Inputs required	5	6
Result	Quadratic Form Value	Solution for x
What it does	Evaluate a quadratic form Q(x) = x^T A x for a symmetric 2×2 matrix and a vector (x₁, x₂). Use it to test whether a matrix is positive definite, negative definite, or indefinite.	Solve a system of two linear equations (ax + by = e and cx + dy = f) instantly. Use it when you need exact values of x and y that satisfy both equations simultaneously.