Johns Hopkins University
Linear Algebra: Linear Systems and Matrix Equations
Johns Hopkins University

Linear Algebra: Linear Systems and Matrix Equations

This course is part of Linear Algebra from Elementary to Advanced Specialization

Taught in English

Joseph W. Cutrone, PhD

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3,254 already enrolled

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Course

Gain insight into a topic and learn the fundamentals

4.7

(31 reviews)

Beginner level

Recommended experience

10 hours (approximately)
Flexible schedule
Learn at your own pace

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Assessments

11 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.7

(31 reviews)

Beginner level

Recommended experience

10 hours (approximately)
Flexible schedule
Learn at your own pace

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This course is part of the Linear Algebra from Elementary to Advanced Specialization
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There are 4 modules in this course

In this module we introduce two fundamental objects of study: linear systems and the matrices that model them. We ask two fundamental questions about linear systems, specifically, does a solution exist and if there is a solution, is it unique. To answer these questions, a fundamental invariant needs to be found. We will use the Row Reduction Algorithm Algorithm to see the number of pivot positions in a matrix. These foundational concepts of matrices and row reduction will be revisited over and over again throughout the course so pay attention to new vocabulary, the technical skills presented, and the theory of why these algorithms are performed.

What's included

2 videos2 readings3 quizzes

In this section we temporarily leave our discussion of linear systems to discuss vectors. These nx1 matrices are used in many contexts in physics, computer science and data science. We show in this section that answering questions about linear combinations turns out to be equivalent to solving a system of linear equations, underlying the deep connections of linear algebra. We then introduce the notion of a matrix as a function on vectors. Questions now about properties of the matrix as a function also turn out to be answered by solving a linear system. These connections between matrices as functions, vectors, and linear systems are sometimes why linear algebra is called the "theory of everything".

What's included

3 videos2 readings3 quizzes

In this module, we study sets of vectors and functions on them. Understanding vectors and how to manipulate them via functions is quite useful in many areas, in particular, physics, computer science, math, and data science. The concept of linear dependence and linear independence is introduced along with the concept of a linear transformation. We will see when a linear transformation T can be represented by a matrix, how to find the matrix, and start to analyze the matrix to extract information about T. Pay careful attention to the new definitions in this section as they will be foundational to future modules!

What's included

3 videos3 readings4 quizzes

In this cumulative assessment, we will ask about the definitions, theorems, and examples shown so far. This is an opportunity to assess your knowledge of the content. The foundational material in this course about linear systems, matrices, and vectors, is key to understanding the more advanced theory and applications of linear algebra to follow. Do the best you can on the assessment and review any questions that are incorrect and learn from them. Good luck!

What's included

1 quiz

Instructor

Instructor ratings
3.3 (7 ratings)
Joseph W. Cutrone, PhD

Top Instructor

Johns Hopkins University
19 Courses393,248 learners

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