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Adding vectors algebraically & graphically
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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 the two ways will always result in the same vector.​​

Subject:
Algebra
Material Type:
Lesson
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
02/28/2018
Defined matrix operations
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Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.

Subject:
Algebra
Material Type:
Lesson
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
02/28/2018
Existence theorems intro
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Overview of the Intermediate Value Theorem, the Extreme Value Theorem and the Mean Value Theorem.

Subject:
Algebra
Material Type:
Lesson
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
02/28/2018
Intro to matrix inverses
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We've learned about matrix addition, matrix subtraction, matrix multiplication. So you might be wondering, is there the equivalent of matrix division? And before we get into that, let me introduce some concepts to you. And then we'll see that there is something that maybe isn't exactly division, but it's analogous to it.

Subject:
Algebra
Material Type:
Lesson
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
02/28/2018
Is matrix multiplication commutative?
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Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). Created by Sal Khan.

Subject:
Algebra
Material Type:
Lesson
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
02/28/2018
Linear Algebra: Another Example of a Projection Matrix
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This 22-minute video lesson shows another example of a projection matrix. It shows how to figure out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.

Subject:
Algebra
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan, Salman
Date Added:
02/20/2011
Linear Algebra: Determinant When Row is Added
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This 17-minute video lesson looks at the determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices).

Subject:
Algebra
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan, Salman
Date Added:
02/20/2011