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Vectors & Linear Algebra Articles: Matrices, Determinants, Rank and Numerical Methods

Vectors and matrices are the common language of circuits, forces and control systems. The articles in this category answer the questions people search for most: how to find a determinant and an inverse, what rank tells you, and which method to use for a large linear system.

Linear algebra Cramer's Rule: How to Use It, Why It Works, and When Not to Use It Cramer's rule explained: replace a column by the constants and divide determinants, 2×2 and 3×3 examples, one unknown, a two-line proof, the Δ = 0… Read the article → Linear algebra 12 Determinant Properties That Appear on Every Exam: det(kA), det(A⁻¹), det(adj A) and the Traps The 12 determinant properties used in entrance exams and engineering mathematics: row operations, det(kA) = kⁿ det A, products, inverses and the… Read the article → Numerical methods Solving Linear Systems Numerically: Gauss, LU, Jacobi or Gauss–Seidel — Which Should You Use? Numerical methods for linear systems compared: Gaussian elimination with pivoting, LU, Cholesky, Jacobi, Gauss–Seidel, SOR, convergence and the… Read the article → Linear algebra Learning Matrices and Determinants: A 7-Step Roadmap from High School and Entrance Exams to Engineering Mathematics A roadmap for matrices, determinants, rank, Cramer's rule and numerical methods: what to learn first, how far entrance exams go, what university… Read the article → Linear algebra What Is the Rank of a Matrix? How to Find It and What It Tells You About a Linear System The rank of a matrix explained visually: finding it by row reduction and by minors, using rank to decide whether Ax = b has one, infinitely many or… Read the article → Linear algebra How to Find the Determinant and Inverse Matrix (2×2 and 3×3) with Examples Learn to find 2×2 and 3×3 determinants by cofactors and the inverse matrix with the adjugate formula, with numeric examples checked by multiplying… Read the article → Vectors Dot Product vs Cross Product: Formulas, Meaning and Examples Compare the dot product (scalar product) and cross product (vector product): formulas, geometric meaning, calculation from components, and how they… Read the article →

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