Science:Math Exam Resources/Courses/MATH307/December 2005/Question 05 (c)

MATH307 December 2005

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Question 05 (c)

Let X be the subspace in three dimensional space $R^{3}$ containing all vectors perpendicular to ${\begin{bmatrix}1\\1\\1\end{bmatrix}}$ Let $L$ be the linear transformation defined by the first projective vector onto the $x-y$ plane and then projecting the resulting vector onto X. If x lies in X then so does $\displaystyle L(x)$. This means that L defines a linear transformation from X to X. Find hte matrix of this transformation with respect to the basis in part (a).

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Hint

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Solution
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