LINEAR ALGEBRA

WHAT WILL WE LEARN?

Yes, we, including me :D

Apps

Linear Algebra Library

SCORING

Midterm 25 % Final 25 % Quiz 10 % Assigned Work 40 %

BOOK

Linear Algebra with Applications 5th edition Keith Nicholson

VECTOR AND VECTOR SPACE

What is vector Combinations of vectors Vector Space

LINEAR MAP

Linear Transformation Scaling, Rotating Skew

Robotics CG Much More!

LINEAR EQUATION

Solving Ax = B

EXAMPLE APPLICATION

Constructing a line passing two points

LINE PASSING TWO POINTS

Line equation ax + by + c = 0

Given the point P1 = (3,5) and P2 = (-1, 2) find the equation a x + b y + c = 0 that passes through the points A and B.

SET UP THE EQUATION

We want to know a,b and c in terms of x and y Know the relation between a,b,c and x,y

MATRIX EQUATION

Solve the equation Ax = B

A = x =

B =

See that b = [0]? We (will soon) know that

Note that Ax = 0 has a nonzero solution if and only if det(a) = 0

We can use cofactor expansion

COFACTOR EXPANSION

It is 3x – 4y + 11 = 0i.e., a = 3, b = -4, c = 11