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

MATH307 April 2006

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Question 07 (a)

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. Find all eigenvalues of the projection P and the reflection R.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint

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Solution
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