235h6 - f ( x,y ) = 0 pass through the point ( x = 2 ,y =...

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Math 235 Assignment 6 Due October 28, 2011 Part I: Webwork. Links for the Webwork part of the homework are on the course web page. Your user name is the part of your student e-mail address before the @ symbol, so if your e-mail address is red@student.umass.edu, then your username is red. Your password is your 8 digit student ID. This week do H6. Part II: 1: Write rotation about an axis through the center of the earth and the point 31 E, 65 N. Your answer should be a product of many matrices. You do not need to perform the matrix multiplication. 2: Assume that M is a 5 × 5 matrix. Can we have ker ( M ) = im ( M )? 3: A cubic is a curve given by an equation of the form f ( x,y ) = a 0 + a 1 x + a 2 y + a 3 x 2 + a 4 xy + a 5 y 2 + a 6 x 3 + a 7 x 2 y + a 8 xy 2 + a 9 y 3 = 0 with a 0 ,a 1 , ··· constants. 3a: Show that requiring that
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Unformatted text preview: f ( x,y ) = 0 pass through the point ( x = 2 ,y = 3) is a linear condition on the coecients a ,a 1 ,a 2 , . 3b: Find a matrix M of size 2 10 so that f ( x,y ) = 0 passes through the points P = (2 , 3) and Q = (-1 , 1) if and only if ( a ,a 1 , ,a 9 ) is in the kernel of M. 3c: Use the rank nullity theorm to nd the possible dimensions of ker ( M ) . You do not need to calculate the RREF of M. Explain why there are innitely many cubics passing through P and Q. 4: Assume that T is a linear transformation from R 7 to R 4 . Use the rank nullity theorem to nd the possible dimensions of ker ( T ) . 1...
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