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Community questions. Learn linear algebra—vectors, matrices, transformations, and more.
- Matrix Transformations
Matrices can be used to perform a wide variety of...
- Matrices for Solving Systems by Elimination Vectors and Spaces
Matrices for Solving Systems by Elimination Vectors and...
- Projections Onto Subspaces
Projections Onto Subspaces - Linear Algebra | Khan Academy
- Transpose of a Matrix
Transpose of a Matrix - Linear Algebra | Khan Academy
- Introduction to Linear Independence
Khan Academy is a nonprofit with the mission of providing a...
- Compositions of Linear Transformations 1
Compositions of Linear Transformations 1 - Linear Algebra |...
- Linear Transformation Examples
Linear Transformation Examples - Linear Algebra | Khan...
- Matrix Vector Products
But what's interesting here is now the product Ax can be...
- Matrix Transformations
Learn the basics of vectors and spaces in linear algebra, such as vector operations, linear combinations, spans, subspaces, bases, dot and cross products, and matrices. Explore examples, practice problems, and proofs with interactive exercises and videos.
- Two-variable linear equations intro. Solutions to 2-variable equations. Worked example: solutions to 2-variable equations.
- x-intercepts and y-intercepts. Intro to intercepts. x-intercept of a line. Intercepts from an equation. (Opens a modal) Intercepts from a table.
- Slope. Intro to slope. Positive & negative slope. Worked example: slope from graph. (Opens a modal) Worked example: slope from two points.
- Horizontal & vertical lines. Slope of a horizontal line. Practice.
However, Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
- 6 min
- Sal Khan
- you guys know they wrote that years ago.
- When we start using matrices we write vectors as columns. So a 2-dimensinoal vector would have 2 rows and 1 column. This can be confusing because p...
- You wouldn't - We simply can't "draw" a vector of more than 3 dimensions. What we can do, however, is use some clever tricks to represent the fourt...
- Yes it is exponentiation, but not in the "standard" notion of multiplication. The multiplication done here is an operation on sets, the operation b...
- if you're already familiar with linear algebra, i would recommend looking through linear algebra again in a more theoretical way, AKA with vector s...
- The Pythagorean theorem can be used with vectors to find the magnitude or length of a vector. The magnitude of a vector is the distance from the or...
- Vectors can represent anything. Usually they represent position in an x, y, and z coordinate, but they're often used to show velocity in the x, y,...
- A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geomet...
- Introduction to algebra. Overview and history of algebra: Introduction to algebra Introduction to variables: Introduction to algebra Substitution and evaluating expressions: Introduction to algebra Evaluating expressions word problems: Introduction to algebra Writing algebraic expressions introduction: Introduction to algebra Introduction to equivalent algebraic expressions: Introduction to algebra Dependent & independent variables: Introduction to algebra.
- Solving basic equations & inequalities (one variable, linear) Algebraic equations basics: Solving basic equations & inequalities (one variable, linear)Why we do the same thing to both sides of an equation: Solving basic equations & inequalities (one variable, linear)One-step addition & subtraction equations: Solving basic equations & inequalities (one variable, linear)One-step multiplication & division equations: Solving basic equations & inequalities (one variable, linear)Two-steps equations intro: Solving basic equations & inequalities (one variable, linear)Two-step equation word problems: Solving basic equations & inequalities (one variable, linear)Linear equations with variables on both sides: Solving basic equations & inequalities (one variable, linear)Linear equations with parentheses: Solving basic equations & inequalities (one variable, linear)
- Linear equations, functions, & graphs. Two-variable linear equations intro: Linear equations, functions, & graphs x-intercepts and y-intercepts: Linear equations, functions, & graphs Slope: Linear equations, functions, & graphs Horizontal & vertical lines: Linear equations, functions, & graphs Intro to slope-intercept form: Linear equations, functions, & graphs Graphing slope-intercept equations: Linear equations, functions, & graphs Writing slope-intercept equations: Linear equations, functions, & graphs.
- Sequences. Introduction to arithmetic sequences: Sequences Constructing arithmetic sequences: Sequences Introduction to geometric sequences: Sequences.
Learn about linear subspaces of Rn, their definition, properties and examples. Watch the video and read the questions and answers from other learners on Khan Academy.
- 23 min
- Sal Khan
Learn about matrices, their operations, inverses, determinants, and applications in this unit of algebra. Practice with exercises, videos, and articles on Khan Academy.
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