Khan Academy
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
Linear Algebra - Khan Academy
Khan Academy offers comprehensive linear algebra lessons, covering topics like vectors, matrices, and transformations.
Adding vectors algebraically & graphically - Khan Academy
To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and …
Khan Academy
Algebra 1; Geometry; Algebra 2; Integrated math 1; Integrated math 2; Integrated math 3; Algebra basics; Trigonometry; Precalculus; High school statistics; Statistics & probability; College algebra; AP®︎/College Calculus AB; AP®︎/College Calculus BC; AP®︎/College Statistics; Multivariable calculus; Differential equations; Linear ...
Vector dot product and vector length (video) | Khan Academy
Definitions of the vector dot product and vector length. ... Middle school Earth and space science; Middle school physics; High school biology. NEW. High school chemistry. NEW. ... Linear algebra. Course: Linear algebra > Unit 1. Lesson 5: Vector dot …
Visualizing a column space as a plane in R3 - Khan Academy
We find out that the null space of A contains more than just the zero vector. It's just the span of these two vectors here, which means that these columns are not linearly independent. We saw that several videos ago.
Vector intro for linear algebra - Khan Academy
A vector has both magnitude and direction. We use vectors to, for example, describe the velocity of moving objects. In this video, you'll learn how to write and draw vectors.
Linear transformations as matrix vector products
Showing how ANY linear transformation can be represented as a matrix vector product
Projections onto subspaces - Khan Academy
If you have some spanning vector, the projection onto this line L that goes through the origin of the vector x, we figured out was x dot your spanning vector for your line, so x dot v over v dot v, which is really just the length of v squared.
Khan Academy
Khan Academy