Science:Math Exam Resources/Courses/MATH307/December 2005/Question 05 (b)
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Question 05 (b)
Let X be the subspace in three dimensional space containing all vectors perpendicular to
Let be the linear transformation defined by the first projective vector onto the plane and then projecting the resulting vector onto X.
Find the matrix that represents as a linear transformation from to
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We need to find the projection matrix.
(Note: [ ] denote matrices)
[projecting vector that projects resulting vector onto X] [projecting vector that projects onto x-y]
To find the projecting vector that projects onto x-y
basis vectors are
where A = 2x2 identity matrix (from our two vectors above)
Therefore: P = 2x2 identity matrix
To find the projecting vector that projects resulting vector onto X:
projecting vector onto the span(a) where
The projecting vector to the orthogonal space =
which is our required projecting matrix</p> <p></p>