Mathematical Examples

Explore how our AI engine breaks down the most complex linear algebra topics into logical, easy-to-follow steps.

Reduced Row Echelon Form (RREF)

Watch the AI systematically apply Gaussian elimination, showing every row swap, scalar multiplication, and row addition to reach the identity matrix.

A = [[1, 2, -1], [2, 1, 4], [3, 3, 4]]

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Eigenvalues & Eigenvectors

See the exact algebraic steps to formulate the characteristic equation det(A - λI) = 0, find its roots, and solve the null space for the eigenvectors.

A = [[4, -2], [1, 1]]

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Singular Value Decomposition (SVD)

Follow the complex process of computing A^T A, finding its eigenvalues to build Σ, and constructing the orthogonal matrices U and V.

A = [[3, 2, 2], [2, 3, -2]]

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Inverse via Adjugate Matrix

Learn to calculate the matrix of minors, find the cofactor matrix, transpose it to get the adjugate, and divide by the determinant.

A = [[2, -1, 0], [-1, 2, -1], [0, -1, 2]]

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Cramer's Rule

Solve a system of linear equations by substituting the constant vector into each column and calculating the ratio of determinants.

3x + y = 5 2x - y = 0

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Gram-Schmidt Process

Watch the AI take a set of linearly independent vectors and construct an orthonormal basis, projecting each new vector onto the existing subspace.

v1=[1,1,0], v2=[1,0,1], v3=[0,1,1]

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