cubes
Khan lecture 1.Khan lecture 2.
# Sum of cubesa³ + b³ = (a + b)(a² - ab + b²)
# Division of cubesa³ - b³ = (a - b)(a² + ab + b²)
Matrix multiplication
IT IS A WHOLE NEW AREA ASIDE FROM MATRICES BASIC OPERATIONS.
Matrices intro
Matrices are just a rectangle array of numbers.Prerequisites: Systems of equations
Matrices
Systems of equations
Cross product
Actually the cross product is very very very limited in use, and as fairly often as the dot product.
cross product
dot product
So don’t waste time on this unless having certain use of it.
REMEMBER: A CROSS PRODUCT ONLY HAS USE IN 3-DIMENSIONS, AND ORDER MATTERS, AND GIVES YOU A…
Vectors multiplication
Vector multiplication is FUNDAMENTAL skill to solve Matrices multiplication.
Matrices multiplication
It’s extending the unit vector idea.
unit vector
Refer to Khan academy article.
In Gilbert Strang’s _Intro to Linear Algebra_, it’s different point of view:
For row form or column form:
Row form
Column form
Vector & basic operations
Definition: vector is a MAGNITUDE with a DIRECTION
Matrix Transformation
It’s a subset of Linear transformation, just with higher dimension rules & multiple points graph multiplying together.
Linear transformation
higher dimension rules
multiple points graph
YOU BREAK THE RULE IN TO DIFFERENT UNIT VECTORS i, j, k... AND BREAK THE GRAPH INTO DIFFERENT POINTS, AND APPLY EACH i, j, k RULES TO EACH POINT.
THE RULE
Composition of Matrix Multiplication
Composition of Matrix Multiplication means More than one linear transformations applies to a graph one by one.
**Although you can see two matrices multiplying together as a transform applying to a graph.But actually sometime you can see it…
a transform applying to a graph
