Textbook: David C. Lay, Linear Algebra and its Applications,  Third Edition.

Chapter 1 Linear Equations
Section 1.1  #  5, 15, 17, 19, 21, 23, 25, 29.
Section 1.2  #  1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 29, 31. Optional: 33.
Section 1.3  #  5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25. Optional: 29, 31.
Section 1.4  #  1, 3, 5, 7 , 9, 13, 15, 17, 19, 21, 23, 25, 35.
Section 1.5  #  1, 3, 5, 7, 9, 11, 17, 19, 23, 27, 29, 31.

Section 1.7  #  1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Optional:  31, 33, 37.
Section 1.8  #  3, 5, 7, 9, 11, 17, 19, 21. Optional: 29, 30, 31, 33.
Section 1.9 #  1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25, 27.

Supplementary exercises: # 3, 7, 14, 23.

Chapter 2 Matrix Algebra
Section 2.1  #  1, 3, 7, 9, 15, 17, 23, 27.
Section 2.2  #  1, 5, 7, 9, 11, 13, 17, 19, 31, 33, 35.
Section 2.3  #  1, 3, 5, 7, 11, 13, 15, 19, 21, 23, 29, 33.
Section 2.8  #  5, 7, 9, 15, 17, 19, 21, 23, 25. Optional: # 31, 33.
Section 2.9  #  3, 5,  9, 11, 13, 15, 19, 21, 25.
Supplementary exercises: # 1, 3, 9. Optional: # 11, 13.

Chapter 3 Determinants
Section 3.1  #  1, 3,  9, 11, 13, 19 - 29, 33 - 39 . (Optional: # 15, 17, 41.)
Section 3.2  #  1, 3, 5, 11 - 19, 27, 29, 37, 39, 41. (Optional: # 31, 33, 35, 43).
Section 3.3  #  1, 3, 7, 9, 11, 17, 21, 23, 27.  (Optional: # 25, 31.)
 

Chapter 5 Eigenvalues and Eigenvectors
Section 5.1 #  1 - 19 (odd), 21, 23. Optional: # 25, 27.
Section 5.2  #  1, 3, 5, 9, 11, 15, 21.
Section 5.3  #  1, 3, 5, 7, 9, 11, 13, 21, 23, 29.
Section 5.5  #  1, 3, 5, 7, 9, 11, 13, 15.

Chapter 6 Orthogonality
Section 6.1  #  1 - 17 (odd), 27.
Section 6.2  #  1, 5, 7, 9, 11, 13, 17, 19, 21. Optional:  27.
Section 6.3  #  1, 3, 7 , 9, 11, 13, 17, 19.