Review for MIDTERM EXAM II( Friday- November 11).


CHAPTER 9  Vector space. Sections 9.6-9.9  
 -Generalized Vector Spaces, inner product, norm 
 -Span and Subspace
 -Bases, Expansions, Dimension
  Review problems:  
  9.6  # 10, 12 a, d
  9.7 # 1 ae, 3, 5ab.
  9.8 # 3 acd, 4, 5. 
  9.9 # 1 ad, 2a, 4bh, 8ah, 9h.
    
 CHAPTER 10: Matrices and Linear  Equations. Sections 101.-10.6 
-Matrices and Matrices Algebra, Transposes: properties
-Block multiplication, Power of a square matrix.  
-Special type of matrices: symmetric, skew symmetric, identity matrix,
-Determinants: cofactor expansion, properties, row operation method. 
-Rank, applications to linear dependence and existence and  uniqueness of linear systems
Review problems: 
10.2 # 8ab, 11a, 12a, 21ac. 
10.3 #  4a, 6, 7a, 9.
10.4 # 2a, 3a, 4a, 7, 9a, 10. 
10.5 # 1 cde, 6a, 8ac,  15. 
10.6 # 1agq, 2g, 5bd.

CHAPTER  11: Eigenvalue Problem. Sections 11.2-11.4
-Know to Find eigenvalues, eigenvectors, eigenspaces for square matrices of dimension two and three. 
-Eigenvalues/eigenvectors properties for symmetric matrices
-Know to find orthogonal bases of eigenvectors for square matrices of dimension two and three. 
-Diagonalization 
 Review problems:
11.2 # 3bjk, 5acd, 6b, 9, 10, 11, 14. 
11.3 #1 abc
11.4 # 1b