Matrix transformations | Linear Algebra | Khan Academy (English)

   Tuesday, July 13, 2021   

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Matrix transformations | Linear Algebra | Khan Academy
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Lecture Description of this above Topic:

Lecture 1: Introduction to the inverse of a function

Lecture 2: 3 x 3 determinant

Lecture 3: Exploring the solution set of Ax = b

Lecture 4: Introduction to projections

Lecture 5: Transpose of a matrix

Lecture 6: Determinant when row multiplied by scalar

Lecture 7: Linear transformations

Lecture 8: Rule of Sarrus of determinants

Lecture 9: Deriving a method for determining inverses

Lecture 10: Preimage and kernel example

Lecture 11: Proof: Invertibility implies a unique solution to f(x)=y

Lecture 12: A more formal understanding of functions

Lecture 13: Transposes of sums and inverses

Lecture 14: Compositions of linear transformations 2

Lecture 15: Showing that A-transpose x A is invertible

Lecture 16: Visualizations of left nullspace and rowspace

Lecture 17: n x n determinant

Lecture 18: Matrix product associativity

Lecture 19: Expressing a projection on to a line as a matrix vector prod

Lecture 20: Matrix condition for one-to-one trans

Lecture 21: Image of a subset under a transformation

Lecture 22: Linear transformations as matrix vector products

Lecture 23: Relating invertibility to being onto and one-to-one

Lecture 24: Simpler 4x4 determinant

Lecture 25: Transpose of a matrix product

Lecture 26: Upper triangular determinant

Lecture 27: Determinant when row is added

Lecture 28: (correction) scalar multiplication of row

Lecture 29: Simplifying conditions for invertibility

Lecture 30: More on matrix addition and scalar multiplication

Lecture 31: Formula for 2x2 inverse

Lecture 32: Determining whether a transformation is onto

Lecture 33: Compositions of linear transformations 1

Lecture 34: Determinant as scaling factor

Lecture 35: Vector transformations

Lecture 36: Duplicate row determinant

Lecture 37: Rotation in R3 around the x-axis

Lecture 38: im(T): Image of a transformation

Lecture 39: Determinant after row operations

Lecture 40: Linear transformation examples: Rotations in R2

Lecture 41: Unit vectors

Lecture 42: Transpose of a vector

Lecture 43: Showing that inverses are linear

Lecture 44: Determinant and area of a parallelogram

Lecture 45: Determinants along other rows/cols

Lecture 46: Distributive property of matrix products

Lecture 47: Matrix vector products as linear transformations

Lecture 48: Rowspace and left nullspace

Lecture 49: Linear transformation examples: Scaling and reflections

Lecture 50: Example of finding matrix inverse

Lecture 51: rank(a) = rank(transpose of a)

Lecture 52: Sums and scalar multiples of linear transformations

Lecture 53: Determinant of transpose

Lecture 54: Matrix product examples

Lecture 55: Surjective (onto) and injective (one-to-one) functions

Lecture 56: Preimage of a set