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.
596 views

Multiplying two 2x2 matrices.
533 views

More on multiplying matrices.
438 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 ...
505 views

Inverting a 3x3 matrix Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ...
539 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 ...
576 views

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

Using matrices to figure out if some combination of 2 vectors can create a 3rd vector
573 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 ...
483 views

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

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

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

Understanding linear combinations and spans of vectors
480 views

More examples determining linear dependence or independence.
541 views

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

Understanding the definition of a basis of a subspace
485 views

Definitions of the vector dot product and vector length
576 views

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

Proving the triangle inequality for vectors in Rn
494 views

Introducing the idea of an angle between two vectors
502 views

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

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

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

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

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

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

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

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

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

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

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

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

Introduction to the notion of vector transformations
550 views

Matrix Vector Products as Linear Transformations
508 views

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

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

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

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

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

More on Matrix Addition and Scalar Multiplication
602 views

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

Linear Transformation Examples: Rotations in R2
420 views

What unit vectors are and how to construct them
442 views

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

Providing the motivation for definition of matrix products
470 views

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

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

Determining whether a transformation is onto
580 views

Exploring the solution set of Ax=b (non homogeneous equations)
604 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)
446 views

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

Determining a method for constructing inverse transformation matrices
478 views

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

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

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

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

A alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus)
595 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
484 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)
569 views

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

Calculating a 4x4 determinant by putting in in upper triangular form first.
469 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
560 views

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

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

Taking the transpose of the product of two matrices
461 views

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

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

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

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