PAU Matemáticas II CV Junio 2026 | Problema 2.1: Álgebra matricial paso a paso

In this video, we solve Problem 2.1 from the Mathematics II exam of the Valencian Community University Entrance Exams (PAU) in June 2026, corresponding to the matrix algebra section. We work with an exercise involving a square matrix dependent on a real parameter and a system of linear equations of the form T · v = u. Solving step by step, we discuss the system according to the parameter's value, apply the Rouché-Frobenius theorem, solve a specific case using Cramer's rule, and calculate the principal stresses from a determinant. 📌 In this video you will see: How to convert a matrix equality into a system of equations. How to analyze a system with a parameter. How to apply the Rouché-Frobenius theorem. How to calculate ranks using determinants and Gaussian elimination. How to distinguish between system of constants, system of inertia, and system of constants. How to solve a system using Cramer's rule. How to calculate the principal stresses using det(T - α · I) = 0. How to interpret the obtained values ​​as eigenvalues ​​of a matrix. Main results: If m ≠ ±2, the system is consistent and has a unique solution. If m = -2, the system is inconsistent and has no solution. If m = 2, the system is consistent and has infinitely many solutions. For m = -1, the solution to the system is (x, y, z) = (4, 4, -2). For m = 2, the principal stresses are α = 0, α = 1, and α = 4. This exercise is very useful for reviewing matrices, systems of linear equations, systems with parameters, matrix rank, Gaussian elimination, Cramer's rule, determinants and eigenvalues, and fundamental content from 2nd year of Baccalaureate Mathematics II and University Entrance Exams. 💙 If you'd like to support the channel: Bizum: 621007935 https://paypal.me/angelcuesta1972 📲 Follow me on social media:   / angel-cuesta-115048070199431     / profesorencasa1   👥 Become a channel member to access full videos and exclusive benefits:    / @angelcuesta