en linear algebra khanacademy 5/5 (1)

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Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Lessons

What a matrix is. How to add and subtract them.
640 views

Multiplying two 2x2 matrices.
573 views

More on multiplying matrices.
473 views

What the inverse of a matrix is. Examples of inverting a 2x2 matrix. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...
546 views

Inverting a 3x3 matrix Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...
585 views

Using Gauss-Jordan elimination to invert a 3x3 matrix. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...
622 views

Using the inverse of a matrix to solve a system of equations.
554 views

Using matrices to figure out if some combination of 2 vectors can create a 3rd vector
607 views

When and why you can't invert a matrix. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...
518 views

Visual intuition of a 3-variable linear equation.
503 views

Solving 3 equations with 3 unknowns (old video from July 2008)
558 views

Visually understanding basic vector operations Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/linear- ...
572 views

Understanding linear combinations and spans of vectors
530 views

More examples determining linear dependence or independence.
593 views

Determining whether 3 vectors are linearly independent and/or span R3
530 views

Understanding the definition of a basis of a subspace
529 views

Definitions of the vector dot product and vector length
610 views

Proving the "associative", "distributive" and "commutative" properties for vector dot products.
574 views

Proving the triangle inequality for vectors in Rn
537 views

Introducing the idea of an angle between two vectors
550 views

Determining the equation for a plane in R3 using a point on the plane and a normal vector
640 views

Proof: Relationship between the cross product and sin of angle between vectors
607 views

Solving a system of linear equations by putting an augmented matrix into reduced row echelon form
590 views

Another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form
740 views

And another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form
591 views

Defining and understanding what it means to take the product of a matrix and a vector
552 views

Showing that the Null Space of a Matrix is a valid Subspace
666 views

Understanding how the null space of a matrix relates to the linear independence of its column vectors
513 views

Figuring out the null space and a basis of a column space for a matrix
627 views

Proof: Any subspace basis has same number of elements
559 views

Showing that linear independence of pivot columns implies linear independence of the corresponding columns in the original equation
618 views

Showing that just the columns of A associated with the pivot columns of rref(A) do indeed span C(A).
618 views

Introduction to the notion of vector transformations
573 views

Matrix Vector Products as Linear Transformations
538 views

Showing how ANY linear transformation can be represented as a matrix vector product
507 views

Exploring what happens to a subset of the domain under a transformation
573 views

Showing that the image of a subspace under a transformation is also a subspace. Definition of the image of a Transformation.
636 views

Example involving the preimage of a set under a transformation. Definition of kernel of a transformation.
558 views

Sums and Scalar Multiples of Linear Transformations. Definitions of matrix addition and scalar multiplication.
542 views

More on Matrix Addition and Scalar Multiplication
627 views

Creating scaling and reflection transformation matrices (which are diagonal)
599 views

Linear Transformation Examples: Rotations in R2
465 views

What unit vectors are and how to construct them
476 views

Expressing a Projection on to a line as a Matrix Vector prod
502 views

Providing the motivation for definition of matrix products
504 views

Proof: Invertibility implies a unique solution to f(x)=y for all y in co-domain of f.
507 views

Relating invertibility to being onto (surjective) and one-to-one (injective)
575 views

Determining whether a transformation is onto
621 views

Exploring the solution set of Ax=b (non homogeneous equations)
630 views

Showing that the rank of the of an mxn transformation matrix has to be an for the transformation to be one-to-one (injective)
485 views

Showing that a transformation is invertible if and only if rref(A) is equal to the identity matrix
480 views

Determining a method for constructing inverse transformation matrices
531 views

Figuring out the formula for a 2x2 matrix. Defining the determinant.
473 views

Determinants: Finding the determinant of a 3x3 matrix
571 views

Defining the determinant for nxn matrices. An example of a 4x4 determinant.
576 views

Finding the determinant by going along other rows or columns
472 views

A alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus)
629 views

Correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant
534 views

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)
602 views

What happens to the determinant when we perform a row operation
523 views

Calculating a 4x4 determinant by putting in in upper triangular form first.
502 views

Realizing that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix
606 views

Viewing the determinant of the transformation matrix as a scaling factor of regions
524 views

Proof by induction that transposing a matrix does not change its determinant
516 views

Taking the transpose of the product of two matrices
516 views

Transpose of a column vector. Matrix-matrix products using vectors
547 views

Relationship between left nullspace, rowspace, column space and nullspace.
498 views

Showing that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n
497 views
 

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