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1.  Say \(A\) is a 5 by 8 matrix. If the dimension of Row(A) is 2, what is the dimension of Col(A)?

a.  2

b.  3

c.  5

d.  6

2.  Say \(A\) is a 5 by 8 matrix. If the dimension of Row(A) is 2, what is the dimension of Nul(A)?

a.  2

b.  3

c.  5

d.  6

3.  Find all the eigenvalues of the matrix $$A = \left[\begin{array}{cc} 1 & 2\\ 2 & 4\end{array}\right]$$

a.  0 and 5

b.  0 and 1 and 2

c.  1 and 5

d.  1 and 2 and 4

For questions 4 through 6, let $$A = \left[\begin{array}{cccc} 1 & 2 & 3 & 4\\ 0 & 1 & 2 & 0\\ 0 & 0 & 2 & 1\\ 0 & 0 & 0 & -2\end{array}\right]$$

4.  Find the eigenvalues for \(A\).

a.  1, 2, 3, 4

b.  0, 1, 2, 3, 4

c.  -2, 0, 1, 2, 3, 4

d.  -2, 1, 2

e.  0, 1, 2

5.  Describe the eigenspace for \(\lambda = 1\).

a.  A line through the origin

b.  Two lines through the origin

c.  A plane through the origin

d.  All of \(R^4\)

e.  Just the zero vector

6.  Which of the standard unit basis vectors are eigenvectors for \(A\).?

a.  Just \(e_1\)

b.  Just \(e_4\)

c.  All of them.

d.  None of them.