Linear Algebra and Geometry 1 — 94% Off Coupon

Systems of equations, matrices, determinants, vectors, and geometry of straight lines and planes in the 3-space

⭐ 4.9 out of 5 Rating (9,305 students) Created by Hania Uscka-Wehlou Updated: April 13, 2026 🌐 English

Key Takeaways

A summarized snapshot of the essential course data, author credentials, and live coupon verification statistics from our manual technical audit.

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Course Title: Linear Algebra and Geometry 1

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Provider: Udemy (Listed via CoursesWyn)

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Instructor: Hania Uscka-Wehlou

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Coupon Verified On: April 13, 2026

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Difficulty Level: All Levels

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Category: Teaching & Academics

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Subcategory: Linear Algebra

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Duration: 47h of on-demand video

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Language: English

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Access: Lifetime access to all course lectures and updates

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Certificate: Official certificate of completion issued by Udemy upon finishing all course requirements

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Top Learning Outcomes: How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work. · Solve systems of linear equations with help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution. · Interpret geometrically solution sets of systems of linear equations by analysing their RREF matrix (row equivalent with the augmented matrix of the system).

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Prerequisites: High-school maths, mainly arithmetic, some Trigonometry · You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody's advantage if you ask your questions on the forum.

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Price: $9.99 with coupon / Regular Udemy price: $179.99. Applying this coupon saves you $170.00 (94% OFF).

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Coupon: Click REDEEM COUPON below to apply discount

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What You'll Learn

The following technical skills represent the core curriculum targets for learners enrolling in this verified program today.

How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work.

Solve systems of linear equations with help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution.

Interpret geometrically solution sets of systems of linear equations by analysing their RREF matrix (row equivalent with the augmented matrix of the system).

Matrix operations (addition, scaling, multiplication), how they are defined, how they are applied, and what computational rules hold for them.

Matrix inverse: determine whether a matrix is invertible; compute its inverse: both with (Jacobi) algorithm and by the explicit formula; matrix equations.

Determinants, their definition, properties, and different ways of computing them; determinant equations; Cramer's rule for n-by-n systems of equations.

Vectors, their coordinates and norm; geometrical vectors and abstract vectors, their addition and scaling: arithmetically and geometrically (in 2D and 3D).

Vector products (scaling, dot product, cross product, scalar triple product), their properties and applications; orthogonal projection and vector decomposition.

Analytical geometry in the 3-space: different ways of describing lines and planes, with applications in problem solving.

Compute distances between points, planes and lines in the 3-space, both by using orthogonal projections and by geometrical reasoning.

Determine whether lines and planes are parallel, and compute the angles between them (using dot product and directional or normal vectors) if they intersect.

How to geometrically interpret n-by-2 and n-by-3 systems of equations and their solution sets as intersection sets between lines in 2D or planes in 3D.

Understand the connection between systems of linear equations and matrix multiplication.

Invertible Matrix Theorem and its applications; apply determinant test in various situations.

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Requirements

Please review the following prerequisites to ensure you have the necessary tools and foundational knowledge for this training.

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High-school maths, mainly arithmetic, some Trigonometry

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You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody's advantage if you ask your questions on the forum.

About This Course

Comprehensive curriculum analysis and educational value proposition from the official provider library hubs.

Linear Algebra and Geometry 1

Systems of equations, matrices, vectors, and geometry

Chapter 1: Systems of linear equations

S1. Introduction to the course

S2. Some basic concepts

You will learn: some basic concepts that will be used in this course. Most of them are known from high-school courses in mathematics, some of them are new; the latter will appear later in the course and will be treated more in depth then.

S3. Systems of linear equations; building up your geometrical intuition

You will learn: some basic concepts about linear equations and systems of linear equations; geometry behind systems of linear equations.

S4. Solving systems of linear equations; Gaussian elimination

You will learn: solve systems of linear equations using Gaussian elimination (and back-substitution) and Gauss--Jordan elimination in cases of systems with unique solutions, inconsistent systems, and systems with infinitely many solutions (parameter solutions).

S5. Some applications in mathematics and natural sciences

You will learn: how systems of linear equations are used in other branches of mathematics and in natural sciences.

Chapter 2: Matrices and determinants

S6. Matrices and matrix operations

You will learn: the definition of matrices and their arithmetic operations (matrix addition, matrix subtraction, scalar multiplication, matrix multiplication). Different kinds of matrices (square matrices, triangular matrices, diagonal matrices, zero matrices, identity matrix).

S7. Inverses; Algebraic properties of matrices

You will learn: use matrix algebra; the definition of the inverse of a matrix.

S8. Elementary matrices and a method for finding A inverse

You will learn: how to compute the inverse of a matrix with Gauss-Jordan elimination (Jacobi’s method).

S9. Linear systems and matrices

You will learn: about the link between systems of linear equations and matrix multiplication.

S10. Determinants

You will learn: the definition of the determinant; apply the laws of determinant arithmetics, particularly the multiplicative property and the expansion along a row or a column; solving equations involving determinants; the explicite formula for solving of n-by-n systems of linear equations (Cramer's rule), the explicite formula for inverse to a non-singular matrix.

Chapter 3: Vectors and their products

S11. Vectors in 2-space, 3-space, and n-space

You will learn: apply and graphically illustrate the arithmetic operations for vectors in the plane; apply the arithmetic operations for vectors in R^n.

S12. Distance and norm in R^n

You will learn: compute the distance between points in R^n and norms of vectors in R^n, normalize vectors.

S13. Dot product, orthogonality, and orthogonal projections

You will learn: definition of dot product and the way you can use it for computing angles between geometrical vectors.

S14. Cross product, parallelograms and parallelepipeds

You will learn: definition of cross product and interpretation of 3-by-3 determinants as the volume of a parallelepiped in the 3-space.

Chapter 4: Analytical geometry of lines and planes

S15. Lines in R^2

You will learn: several ways of describing lines in the plane (slope-intercept equation, intercept form, point-vector equation, parametric equation) and how to compute other kinds of equations given one of the equations named above.

S16. Planes in R^3

You will learn: several ways of describing planes in the 3-spaces (normal equation, intercept form, parametric equation) and how to compute other kinds of equations given one of the equations named above.

S17. Lines in R^3

You will learn: several ways of describing lines in the 3-space (point-vector equation, parametric equation, standard equation) and how to compute other kinds of equations given one of the equations named above.

S18. Geometry of linear systems; incidence between lines and planes

You will learn: determine the equations for a line and a plane and how to use these for computing intersections by solving systems of equations.

S19. Distance between points, lines, and planes

You will learn: determine the equations for a line and a plane and how to use these for computing distances.

S20. Some words about the next course

You will learn: about the content of the second course.

Make sure that you check with your professor what parts of the course you will need for your final exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.

A detailed description of the content of the course, with all the 222 videos and their titles, and with the texts of all the 175 problems solved during this course, is presented in the resource file

“001 Outline_Linear_Algebra_and_Geometry_1.pdf”

under Video 1 ("Introduction to the course"). This content is also presented in Video 1.

Meet Your Instructor

Academic background and professional track record of the subject matter expert responsible for this curriculum.

Hania Uscka-Wehlou

Verified Architect

A global leader with specialized excellence in Teaching & Academics. Instructors are vetted for curriculum quality, responsiveness, and consistent student success across the Udemy platform.

4.8 / 5.0

Instructor Rating

94% +

Success Rate

Course Comparison

Market-relative value analysis comparing this verified instructor deal against professional subscription and retail averages.

Feature Benchmarks	This Verified Offer	Global Standard
Cost Verification	FREE (100% Validated)	Fixed Subscription Fee
Enrollment Type	Professional Lifetime Access	Limited Time Ownership
Certification Award	Included with Access Code	Required Add-on Fee

Expert Review

Andrew Derek

Lead Course Analyst, CoursesWyn

"After auditing the curriculum depth and verifying the live access protocol, Linear Algebra and Geometry 1 stands as an essential career asset. For a verified cost of $0, the return-on-learning ratio far exceeds commercial alternatives."

✅ Strategic Advantages

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Official Certificate: Credential generated at no cost.
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Mobile Friendly: Full access via smart TV & mobile.
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Expert Pacing: Modular design for professional schedules.

❌ Considerations

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Technical Depth: Requires focused 10+ hours study.
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Tool Prep: Certain labs require proprietary software setups.

Verification Outcome: Exceptional Academic Value

Course Rating

Collective learner data and performance analytics based on verified alumni feedback loops and technical graduation audits.

4.9

★★★★★

Verified Excellence

5 Stars

88%

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Frequently Asked Questions

Curated answers to the most frequent learner inquiries regarding availability, certification, and enrollment logic protocols.

Andrew Derek

Expert Reviewer

Andrew Derek is a lead editor and course analyst at CoursesWyn with over 8 years of experience in online education and digital marketing. He meticulously audits every Udemy coupon and course syllabus to ensure students get the highest quality learning materials at the best possible price.

Contact Andrew • Verified by CoursesWyn Editorial Team

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