Fall Linear Algebra Midterm II

Fall Linear Algebra Midterm II - MATH1850/2050 S09 Name:...

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MATH1850/2050 S09 Name: Page 1 of 7 (1) (5 marks) Find an equation of the plane containing the point P (1 , 1 , 1) and parallel to the two lines given by the parametric equations l 1 : x = 1 - t, y = 2 + 2 t, z = 3 l 2 : x = 3 - 2 t, y = 4 + t, z = t (2) (5 marks) Say T : R 3 R 3 is the linear operator defined by: a reflection about the xy -plane followed by a counter-clockwise rotation by an angle of π/ 2 about the positive x -axis followed by an othogonal projection onto the yz -plane. Use [ T ] = [ T ( e 1 ) | T ( e 2 ) | T ( e 3 )] to get the standard matrix of T .
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Name: Page 2 of 7 (3) (7 marks) (a) (4 marks) Let T : R 3 R 3 be the linear operator defined below. De- termine the values of k for which T fails to be one-to-one. w 1 = 2 x 1 + x 2 + 2 x 3 w 2 = - 2 x 1 + kx 2 + 2 x 3 w 3 = 2 x 1 + ( k + 2) x 2 + ( k + 1) x 3 (b) (3 marks) Let T : R 2 R 2 be the one-to-one linear transformation defined by T ( x 1 ,x 2 ) = (2 x 1 - x 2 , 5 x 1 - 3 x 2 ) . Find the standard matrix [
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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Fall Linear Algebra Midterm II - MATH1850/2050 S09 Name:...

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