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Unformatted text preview: 1 IMPORTANT NOTE: These IMPORTANT NOTE: These are the answers. In the are the answers. In the exam you need to add justifcations exam you need to add justifcations Example (3.327) Determine whether the following vectors form a basis of R 4 (1,1,1,1), (1,1,1,1),(1,2,4,8),(1,2,4,8) Answer: Yes, (the matrix with these vectors as columns is invertible) Exercise 1.230 Find the polynomial of degree 3 whose graph passes through the points (0,1),(1,0),(1,0), (2,15) Find the inverse of the rotation matrix. cos(a)sin(a) sin(a) cos(a) cos(a) sin(a)sin(a) cos(a) Answer= Let T be a clockwise rotation in R 2 by /2 followed by an orthogonal projection onto the y axis. 1. Find the matrix of T. 2. Determine whether T is invertible 3. Find im(T) and ker(T) Answer: It was given in class. Find the inverse of the matrix and check your answer. Interpret your result geometrically. a b ba a b ba Answer: The matrix is a reection about a line L followed by a scaling by (a 2 + b 2 ) 1/2 ....
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This note was uploaded on 09/14/2011 for the course MAT 211 taught by Professor Movshev during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 MOVSHEV
 Vectors

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