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Unformatted text preview: A is also a basis for the image. 2. Find a matrix A so that the image of the transformation T ( x ) = Ax from R 2 to R 3 is the plane through the origin with normal vector (1 , 1 , 1). Solution. That plane is the set of linear combinations of (1 , ,-1) and (1 ,-1 , 0), since they are both perpendicular to (1 , 1 , 1) and are linearly independent. So A = 1 1-1-1 will work. There are, of course, many other choices. You can take the columns of A to be any pair of linearly independent vectors that are perpendicular to (1 , 1 , 1)....
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This note was uploaded on 02/06/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
- Fall '08