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1.  Let \(\left[\begin{array}{cc} 1 & 1 \\ 0 & 1\end{array}\right]\). Is \(A\) diagonalizable?

a.  Yes.

b.  No, because it has too few eigenvalues.

c.  No, because there aren't two linearly independent eigenvectors.

2.  Let \(\left[\begin{array}{cc} 1 & 0 \\ 0 & 1\end{array}\right]\). Is \(A\) diagonalizable?

a.  Yes.

b.  No, because it has too few eigenvalues.

c.  No, because there aren't two linearly independent eigenvectors.

3.  Say \(T:{\bf R}^2 \rightarrow {\bf R}^2\) is the linear transformation which reflects the plane over some line through the origin (you don't need to know which line, and you don't need to know the 2 by 2 matrix \(A\) such that \(T(\vec{x}) = A\vec{x}\)). What are the eigenvalues of T (Just think about it)?

a.  There are none

b.  Only 1

c.  Only -1

d.  1 and -1

c.  1 and 0

4.  Say \(T:{\bf R}^2 \rightarrow {\bf R}^2\) is the linear transformation which rotates the plane by 45 degrees around the origin. What are the eigenvalues of T (Just think about it)?

a.  There are none

b.  Only 1

c.  Only -1

d.  1 and -1

c.  1 and 0

5.  Say \(T:{\bf R}^2 \rightarrow {\bf R}^2\) is the linear transformation which rotates the plane by 180 degrees around the origin. What are the eigenvalues of T (Just think about it)?

a.  There are none

b.  Only 1

c.  Only -1

d.  0 and 1

c.  1 and 0

6.  Say \(T:{\bf R}^3 \rightarrow {\bf R}^3\) is the linear transformation which rotates three dimensional space by 45 degrees around some line through the origin. What are the eigenvalues of T (Just think about it)?

a.  There are none

b.  Only 1

c.  Only -1

d.  1 and -1

c.  1 and 0

7.  Consider the triangle with vertices A(1,2,3), B(5,5,3), and C(3,4,4). Find cos\(\theta\) where \(\theta\) is the smallest angle in the triangle.

a.  -14/15

b.  -1/15

c.  0

d.  1/15

e.  14/15