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

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Presentation transcript:

L INEAR A LGEBRA

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

S CORING Midterm25 % Final25 % Quiz10 % Assigned Work40 %

B OOK Linear Algebra with Applications 5 th edition Keith Nicholson

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

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

L INEAR E QUATION Solving Ax = B

E XAMPLE A PPLICATION Constructing a line passing two points

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.

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

M ATRIX E QUATION 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

C OFACTOR E XPANSION

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