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MAT224H1 (138)
Lecture

Drawing planar quadratic, quadratic forms, orthonormal basis and matricies, gram-schmidt orthogonalization process

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Department
Mathematics
Course
MAT224H1
Professor
Martin, Burda
Semester
Winter

Description
Lecture 9 notes by Y. Burda 1 Drawing a planar quadric We all know what the equation x + y = 1 describes: it is the equation of a unit circle: (x,y) 1 x y2 It is easy to see what shape is described by the equation 9 + 4 = 1. If a point (x,y) lies on this shape, then the point (x3,y2) lies on the unit circle. So in fact what we have is the result of stretching the unit circle by a factor of 3 in the x direction and by a factor of 2 in y direction. The resulting shape is called an ellipse. (x,y) (x3,y2) Much harder is to describe how the locus of points (x,y) satisfying 3x + 2 4xy +3y = 1 looks like. In fact we will spend the next two lectures learning 1 www.notesolution.com
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