# Science:Math Exam Resources/Courses/MATH307/April 2006/Question 07 (c)

MATH307 April 2006

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### Question 07 (c)

Let P be the projection of all vectors in $\mathbb {R} ^{4}$ into R(A) which is the column space of the matrix

${\begin{bmatrix}1&0\\-1&1\\1&1\\0&-2\end{bmatrix}}$ .

Let R be the reflection in R(A). Answer the following questions with little or no calculation. You do not need to find the projection and the reflection matrices to answer these questions.

For the projection P, determine the relation between its row space and its column space and the relation between its nullspace and left nullspace. Then find a basis for each one of the four fundamental subspaces.

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