# 69 Results

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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
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Author:
Salman Khan
02/28/2018
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Describe a bivariate relationship's linearity, strength, and direction. In other words, plotting things that take two variables into consideration and trying to see whether there's a pattern with how they relate.

Subject:
Statistics and Probability
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018
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This is a brief conditional probability examplediscussing probabilities like P(A | B) using breakfast and lunch as examples.

Subject:
Statistics and Probability
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018
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This video talka about what is easily one of the most fundamental and profound concepts in statistics and maybe in all of mathematics. And that's the central limit theorem.

Subject:
Statistics and Probability
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018
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Understanding alternate coordinate systems. Created by Sal Khan.

Subject:
Algebra
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Lesson
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Author:
Salman Khan
02/28/2018
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Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise).

Subject:
Statistics and Probability
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Lesson
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Author:
Salman Khan
02/28/2018
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Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.

Subject:
Algebra
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Lesson
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Author:
Salman Khan
02/28/2018
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Sociology often looks at different age cohorts. A cohort is simply a group of people, but here we're looking specifically at different age groups or generations, because these people all lived through the same certain events through a certain time that affected their lives similarly.

Subject:
Sociology
Material Type:
Lesson
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Author:
Sydney Brown
02/28/2018
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Dimension of the Column Space or Rank. Created by Sal Khan.

Subject:
Algebra
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Lesson
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Author:
Salman Khan
02/28/2018
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Dimension of the Null Space or Nullity. Created by Sal Khan.

Subject:
Algebra
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Lesson
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Author:
Salman Khan
02/28/2018
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This video defines the differences between discrete and continuous random variables, then works through examples of each.

Subject:
Statistics and Probability
Material Type:
Lesson
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02/28/2018
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Where we live in society plays a huge role in the environmental benefits and risks that we're exposed to.

Subject:
Sociology
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Lesson
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02/28/2018
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Compare distributions using the features of shape, center, spread, and outliers.

Subject:
Statistics and Probability
Material Type:
Lesson
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02/28/2018
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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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Lesson
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Author:
Salman Khan
02/28/2018
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Short video which describes the difference between a sample and a population.

Subject:
Statistics and Probability
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Lesson
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Author:
Salman Khan
02/28/2018
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Sal shows examples of intersection and union of sets and introduces some set notation.

Subject:
Statistics and Probability
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018
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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
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Lesson
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Author:
Salman Khan
02/28/2018
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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
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Lesson
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Author:
Salman Khan
02/28/2018
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This 10-minute video lesson looks at Determinants: Finding the determinant of a 3x3 matrix.

Subject:
Algebra
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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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
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Author:
Khan, Salman
02/20/2011
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This 15-minute video lesson sees that orthonormal bases make for good coordinate systems.

Subject:
Algebra
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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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
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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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
Material Type:
Lecture
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Author:
Salman Khan
02/20/2011
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This 25-minute video lesson introduces the idea of an angle between two vectors.

Subject:
Algebra
Material Type:
Lecture
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Author:
Salman Khan
02/20/2011
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This 10-minute video lesson looks at what happens to the determinant when we perform a row operation.

Subject:
Algebra
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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This 13-minute video lesson looks at the determinant when a row is multiplied by a scalar.

Subject:
Algebra
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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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
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Author:
Khan, Salman
02/20/2011
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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
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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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
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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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
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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This 9-minute video lesson shows how to find the determinant by going along other rows or columns.

Subject:
Algebra
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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This 19-minute video lesson provides dot and cross product comparison and Intuition.

Subject:
Algebra
Material Type:
Lecture
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Author:
Salman Khan
02/20/2011
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This 8-minute video lesson looks at the determinant of a matrix with duplicate rows.

Subject:
Algebra
Material Type:
Lecture
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Provider Set:
Author:
Khan, Salman
02/20/2011
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This video shows an example using orthogonal change-of-basis matrix to find transformation matrix

Subject:
Algebra
Material Type:
Lecture
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02/20/2011
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This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.

Subject:
Algebra
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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This 18-minute video lesson shows how to figure out the formula for a 2x2 matrix. And it defines the determinant.

Subject:
Algebra
Material Type:
Lecture
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Author:
Khan, Salman
02/20/2011
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This 13-minute video lesson uses Gram-Schmidt to find an orthonormal basis for a plane in R3.

Subject:
Algebra
Material Type:
Lecture
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Provider Set:
Author:
Khan, Salman
02/20/2011
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This 12-minute video lesson looks at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other.

Subject:
Algebra
Material Type:
Lecture
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Provider Set:
Author:
Khan, Salman
02/20/2011
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This 3-minute video lesson looks at the orthogonal complement of the nullspace and left nullspace.

Subject:
Algebra
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
02/20/2011
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This video shows how to find that the orthogonal complement of the orthogonal complement of V is V

Subject:
Algebra
Material Type:
Lecture
Provider: