VIDEO
HIGHLIGHT
Log InSign up
✔️ Regla de CRAMER para resolver SISTEMAS de Ecuaciones 3x3 Ejercicios resueltos [ Bachillerato Uni
SummaryTranscriptChat

✔️ Regla de CRAMER para resolver SISTEMAS de Ecuaciones 3x3 Ejercicios resueltos [ Bachillerato Uni

Introduction to Cramer's Rule

Overview of the Lesson

  • The video introduces Cramer's Rule, a systematic method for solving systems of equations. It highlights its importance and potential challenges in application.

Transition to Matrix Form

  • The first step involves converting systems of equations into matrix form, which simplifies the representation by eliminating variables like x, y, and z. This is crucial for applying Cramer’s Rule effectively.

Understanding Matrices

Coefficient Matrix

  • The coefficient matrix consists of numbers multiplying the unknowns (e.g., 2, 1, 1 for x, y, z). It's essential to correctly identify these coefficients when forming matrices.

Augmented Matrix

  • An augmented matrix combines the coefficient matrix with the constants from the equations. This format aids in visualizing and manipulating systems of equations more efficiently.

Calculating Determinants

Importance of Determinants

  • Before applying Cramer’s Rule, calculating the determinant of the coefficient matrix (denoted as A) is necessary; it must be non-zero for solutions to exist using this method. If zero, alternative methods are required.

Step-by-Step Calculation

  • The video demonstrates how to calculate determinants using a specific technique involving diagonals and signs (+/-), emphasizing careful execution to avoid common mistakes related to sign errors.

Applying Cramer's Rule

Systematic Procedure for Variables

  • Once confirmed that the determinant is non-zero, a systematic approach follows:
  • For each variable (x, y, z), replace corresponding columns in A with constant terms from equations.
  • Calculate new determinants based on these modified matrices before dividing by the original determinant of A.

Example Calculations

Calculating Determinants and Applying Cramer's Rule

Importance of Visual Learning in Mathematics

  • The speaker emphasizes the significance of visual aids in understanding mathematical concepts, particularly when calculating determinants. A clear visual representation helps in retaining information.
  • The example provided involves calculating a determinant and dividing it by the determinant of the coefficient matrix, illustrating practical application.

Self-Verification Techniques During Exams

  • The speaker discusses self-verification methods during exams to ensure accuracy and confidence in answers, suggesting that knowing one has secured points is beneficial for reducing anxiety.
  • A method proposed includes substituting variables with their values to check if the results align with expected outcomes, reinforcing understanding through practice.

Step-by-Step Verification Process

  • The speaker prefers to perform checks on the last equation after substitution for efficiency, ensuring calculations are correct before finalizing answers.
  • If discrepancies arise during verification, revisiting calculations is crucial; attention to detail can prevent errors from affecting overall results.

Transitioning to Matrix Representation

  • Moving forward, the discussion shifts towards expressing systems in matrix form as a foundational step for further calculations.
  • The importance of understanding determinants is reiterated; they must be non-zero for applying Cramer’s Rule effectively.

Properties of Determinants

  • The speaker explains that if a determinant equals zero due to identical rows or columns, it indicates that solutions may not exist or are infinite.
  • Emphasis is placed on recognizing patterns within matrices (e.g., identical columns), which can simplify calculations significantly and save time.

Application of Cramer's Rule

  • When applying Cramer’s Rule, it's essential first to calculate determinants accurately; mistakes here can complicate problem-solving efforts.
  • For each variable (like x and y), changing corresponding columns while maintaining structure allows for systematic solving using determinants.

Understanding Determinants in Mathematics

Calculating Determinants

  • The speaker discusses the calculation of a determinant, indicating that it equals zero. They mention the arrangement of columns for variables x1, x2, and z.
  • The speaker notes that their mathematical intuition recognizes that the current determinant is identical to a previously calculated one, which also resulted in -4.
  • Emphasizing the importance of recognizing patterns in determinants, they suggest that this skill is often tested in exams to assess students' understanding.

Properties of Determinants

  • The speaker explains how having two identical columns (column 1 and column 3) leads to a determinant value of zero. This demonstrates knowledge of determinant properties during examinations.
  • They highlight the significance of demonstrating mathematical knowledge on exams, as it influences grading based on perceived understanding rather than actual knowledge.

Verification Process

  • The discussion shifts to verifying calculations by substituting values into equations. The speaker emphasizes self-checking as crucial before finalizing answers for exams.
Video description

👉 En el vídeo aprenderemos el 🔥 METODO de CRAMER para resolver sistemas de tres ecuaciones con tres incógnitas , Sistemas compatibles determinados SCD , matemáticas 2º bachillerato Universidad ejemplos y Ejercicios resueltos paso a paso desde cero Responderemos a las siguientes preguntas Qué es la regla de Cramer Cuando usar la regla de Cramer Podremos usar las regla de cramer en los sistemas de tres ecuaciones con tres incógnitas , cuando el determinante de la matriz de coeficientes A sea distinto de cero , es decir que el sistema es compatible determinado Para usar el método de Cramer , primero calculamos el determinante de la matriz de coeficientes , que es el determinante del denominador , El determinante de el numerador es el que resulta de sustituir la columna de la variable a calcular por la columna de los términos independientes Lista de reproducción de Matrices Determinantes y sistemas de ecuaciones https://www.youtube.com/playlist?list=PLunRFUHsCA1xNJCafu2Tf2tD13b8Wz5hH si te ha servido , dale al *LIKE SUSCRIBETE* http://goo.gl/CMFnu0 y activa la campanilla , compártelo por las redes sociales y grupos de clase ;) Sigue el curso *geometría en el espacio*https://www.youtube.com/playlist?list=PLunRFUHsCA1yH3sJP2VgsPij4jCceo6YQ Lista de reproducción de campo eléctrico https://www.youtube.com/playlist?list=PLunRFUHsCA1wnOUjaPSWY8UVT6MqanGxD Lista de reproducción INTEGRALES https://www.youtube.com/playlist?list=PLunRFUHsCA1xnGhUtgzSsBHTzmoFeWdYC Lista de reproducción campo gravitatorio https://www.youtube.com/playlist?list=PLunRFUHsCA1zoXLbkloPKDUQ5f5t25BHo Lista de reproducción Equilibrio Químico https://www.youtube.com/watch?v=8B16zGe99VE&list=PLunRFUHsCA1x9vgJ5VukNBEkNofia9HGo Formularios Profesor10demates https://www.youtube.com/playlist?list=PLunRFUHsCA1xlQ8hRJcGon7UoDSDzT_hs Lista de reproducción Movimiento Ondulatorio https://www.youtube.com/watch?v=WOv4JOk1mjo&list=PLunRFUHsCA1xApSdpQQb3eSCqcEb-OHhY *Regla de lHopital* https://www.youtube.com/watch?v=UgyzVRS7ukA&list=PLunRFUHsCA1zHaYFyPsO6gXhBhqchox1x 00:00 Introducción METODO DE CRAMER 00:17 Regla de CRAMER ejercicio resuelto a) 09:15 Regla de CRAMER ejercicio resuelto b)