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

MATH307 December 2005

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### Question 05 (b)

Let X be the subspace in three dimensional space ${\displaystyle \mathbb {R} ^{3}}$ containing all vectors perpendicular to ${\displaystyle {\begin{bmatrix}1\\1\\1\end{bmatrix}}}$

Let ${\displaystyle L}$ be the linear transformation defined by the first projective vector onto the ${\displaystyle x-y}$ plane and then projecting the resulting vector onto X.

Find the ${\displaystyle 3x3}$ matrix that represents ${\displaystyle L}$ as a linear transformation from ${\displaystyle \mathbb {R} ^{3}}$ to ${\displaystyle \mathbb {R} ^{3}}$

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