1. L INEAR A LGEBRA

2. W HAT WILL WE LEARN ? Yes, we, including me :D Apps Linear Equation Vector Spaces Linear Map Vectors, Matrix Linear Algebra Library

3. S CORING Midterm25 % Final25 % Quiz10 % Assigned Work40 %

4. B OOK Linear Algebra with Applications 5 th edition Keith Nicholson

5. V ECTOR AND V ECTOR S PACE What is vector Combinations of vectors Vector Space

6. L INEAR M AP Linear Transformation Scaling, Rotating Skew Robotics CG Much More!

7. L INEAR E QUATION Solving Ax = B

8. E XAMPLE A PPLICATION Constructing a line passing two points

9. L INE P ASSING T WO P OINTS 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.

10. S ET UP THE E QUATION We want to know a,b and c in terms of x and y Know the relation between a,b,c and x,y

11. M ATRIX E QUATION Solve the equation Ax = B A = x = B =

12. 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

13. C OFACTOR E XPANSION

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