PAU Matemáticas II CV Junio 2026 | Problema 2.2: Matrices ortogonales paso a paso

In this video, we solve Problem 2.2 from the Mathematics II exam of the Valencian Community University Entrance Exams (PAU) in June 2026, corresponding to the matrix algebra section. We work on an exercise focused on orthogonal matrices. First, we verify that a trigonometric matrix is ​​orthogonal for any real value of the parameter. Then, we determine the parameter values ​​for which another matrix is ​​orthogonal, and finally, we solve a matrix equation using the fundamental property of this type of matrix: its inverse is equal to its transpose. 📌 In this video you will see: What it means for a matrix to be orthogonal. How to verify that a matrix satisfies A · A^T = I. How to use the trigonometric identity sin^2(α) + cos^2(α) = 1. How to determine parameters for a matrix to be orthogonal. How many orthogonal matrices exist for a given matrix form. How to solve for a variable in a matrix. How to use the fact that if B is orthogonal, then B⁻¹ = Bᵀ. How to obtain all the solution matrices of a matrix equation. Main results: Matrix A is orthogonal for all real values ​​of alpha. For matrix B to be orthogonal, a = ±1 and b = ±1 must hold. There are 4 orthogonal matrices of the form shown. The matrix equation has 4 solution matrices, one for each possible combination of a and b. This exercise is very useful for reviewing orthogonal matrices, transposes, inverses, matrix multiplication, the fundamental trigonometric identity, and matrix equations—important topics in Mathematics II for the second year of high school 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