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 ) = A⃗x 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 = 1 111 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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 Fall '08
 lee
 Linear Algebra, Vectors, linearly independent vectors, linearly independent set

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