Description

Linear Algebra and Geometry 1: Master Systems, Matrices, Vectors, and Geometry

Requirements:

• High school-level mathematics, primarily arithmetic and some trigonometry

• No prior university-level experience required

• Students are encouraged to ask questions during lectures for clarification—your doubts benefit everyone!

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Course Overview

Linear Algebra and Geometry 1 is a comprehensive course designed to build a strong foundation in linear algebra and analytic geometry. Through a combination of theory, practical examples, and solved problems, you will learn how to work with systems of equations, matrices, vectors, and geometric concepts in 2D and 3D spaces.

This course is ideal for university and college engineering students as well as anyone looking to strengthen their mathematics skills for applications in science, engineering, and technology.

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What You Will Learn

Chapter 1: Systems of Linear Equations

• Introduction to Linear Algebra and Geometry: Overview of key concepts used in the course, including topics from high school math and new concepts introduced gradually.

• Systems of Linear Equations: Understand linear equations, geometric interpretations, and systems of equations in multiple variables.

• Gaussian and Gauss-Jordan Elimination: Solve systems of linear equations, including unique, inconsistent, and infinitely many solutions.

• Applications: Learn how linear systems are applied in mathematics, physics, and natural sciences.

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Chapter 2: Matrices and Determinants

• Matrices and Matrix Operations: Learn matrix addition, subtraction, scalar multiplication, and matrix multiplication. Explore different types of matrices including square, triangular, diagonal, zero, and identity matrices.

• Matrix Inverses and Algebraic Properties: Understand matrix algebra and compute inverses of non-singular matrices.

• Elementary Matrices and Gauss-Jordan Method: Master practical methods for finding matrix inverses.

• Linear Systems and Matrices: Explore the connection between matrices and systems of linear equations.

• Determinants: Learn determinant properties, computation, and applications in solving systems of equations using Cramer’s Rule.

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Chapter 3: Vectors and Their Products

• Vectors in 2D, 3D, and n-Dimensional Spaces: Learn vector arithmetic, graphical representation, and operations in Rⁿ.

• Distance and Norms: Calculate distances between points and norms of vectors; normalize vectors.

• Dot Product and Orthogonality: Understand dot products, compute angles between vectors, and project vectors onto others.

• Cross Product: Learn cross product operations and use 3×3 determinants to compute volumes of parallelepipeds.

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Chapter 4: Analytical Geometry of Lines and Planes

• Lines in R²: Explore slope-intercept, intercept, point-vector, and parametric forms; convert between different representations.

• Planes in R³: Study normal equations, intercept form, and parametric equations of planes.

• Lines in R³: Learn multiple representations of lines in 3D space and compute intersections.

• Geometry of Linear Systems: Solve problems involving intersections of lines and planes.

• Distance Calculations: Compute distances between points, lines, and planes.

• Next Steps: Overview of content in the follow-up course.

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Course Features

• 222 Video Lectures covering every topic in detail

• 175 Solved Problems to reinforce your understanding

• Interactive Q&A for doubt clearance

• Real-world applications in engineering and natural sciences

Make sure to confirm with your professor which parts of the course are required for your exams, as it may vary by institution or year.

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Who This Course is For:

• University and college engineering students

• Anyone aiming to strengthen foundational knowledge in linear algebra and geometry for higher studies or professional applications

Please Note: Files will be included in this purchase only Full Course Video & Course Resources. You will get cloud storage download link with life time download access.