12. What are the eigenvalues of the matrix


A. {-5, 1}B. {-1, 5} C. {-4,-2} D. {1, 3}E.{ 2+i sqrt(7) , 2 - i sqrt(7)

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13. Let


For which of the vectors w does {u, v, w} form an orthogonal basis for R3 ?

A.

B

C.

D.

E

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14. Let be a basis for R4 and let L : R4 -> R2 be a linear transformation such that


What is the dimension of the kernel of L?

A. 0B. 1
C. 2
D. 3E. 4

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15. Let


What is the determinant of A?

A. -4
B. -3
C. -2
D. -1
E. 0

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16. Which of the following is a basis for the subspace of R3 generated by the vectors



A

B

C

D

E

Four vectors cannot span a subspace of R3

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17. Let T: R2 -> R2 be the linear transformation defined by


What is the matrix associated with this transformation with respect to standard bases?

A

B

C

D

E

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18. Let


What is the entry on the first column of the third row of A-1 ?

A. -3B. -1 C. -1/2D. 1 E. 2

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19. Let

What is the determinant of A?

A. -2B. -1 C. 0D. 1 E. 2

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20. Let


Which of the following is a basis for the subspace of R3 generated by the eigenvectors of A corresponding to the eigenvalue 6:

A

B

C

D

E

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21. Let T be the linear transformation from R3 to R3 whose matrix with respect to the standard bases is


What is the value of (p, q, r)Transpose for which


A

B

C

D

E

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22. What is the value of the determinant

where

A. -2B. -1 C. 0D. 1 E. 2

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23. Let M be the subspace in R4 generated by the vectors


Let N be the subspace in R4 generated by the vectors


Let V be the inersection of the subspaces M and N. Which of the following pairs of vectors constitutes a basis for V?

A

B

C

D

E

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24. Let A be a square matrix whose characteristic polynomial is


What is the determinant of A?

A. -1B. -1/2 C. 0D. 1/2 E. 1

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