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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
Mathematics
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Understanding alternate coordinate systems. Created by Sal Khan.

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Mathematics
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Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.

Subject:
Algebra
Mathematics
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Dimension of the Column Space or Rank. Created by Sal Khan.

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Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Dimension of the Null Space or Nullity. Created by Sal Khan.

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Algebra
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Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Overview of the Intermediate Value Theorem, the Extreme Value Theorem and the Mean Value Theorem.

Subject:
Algebra
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Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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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
Mathematics
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Lesson
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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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
Mathematics
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Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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This 10-minute video lesson looks at Determinants: Finding the determinant of a 3x3 matrix.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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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
Mathematics
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Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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This 15-minute video lesson sees that orthonormal bases make for good coordinate systems.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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This 3-minute video lesson is a correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Salman Khan
02/20/2011 Conditional Remix & Share Permitted
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This 25-minute video lesson introduces the idea of an angle between two vectors.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Salman Khan
02/20/2011 Conditional Remix & Share Permitted
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This 10-minute video lesson looks at what happens to the determinant when we perform a row operation.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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This 13-minute video lesson looks at the determinant when a row is multiplied by a scalar.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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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
Mathematics
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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This 22-minute video lesson realizes that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix.

Subject:
Algebra
Mathematics
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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This 20-minute video lesson shows how to view the determinant of the transformation matrix as a scaling factor of regions.

Subject:
Algebra
Mathematics
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Lecture
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Author:
Khan, Salman
02/20/2011 Conditional Remix & Share Permitted
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This 14-minute video lesson shows the proof by induction that transposing a matrix does not change its determinant.

Subject:
Algebra
Mathematics
Material Type:
Lecture
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