Review for MIDTERM EXAM II(Tuesday -November 22).

CHAPTER 3, Real  Vector Space. Section: 3.8 
-Rank of a matrix
-Theorem 3.20 (page 210)
- Rank Theorem (page 211)
-Review problems:
 3.8 # 13a, 17a, 26, 28, 29, 39. 
 
 CHAPTER 4 INNER PRODUCT SPACES. Sections: 4.1, 4.3, 4.4, 4.5
-Length, inner product and magnitude in 2D and 3D.  
- Inner product spaces. 
  Definition, properties, distance, orthogonality, Cauchy-Schwarz  inequality 
-The Gram-Schmidt Process  
- Projection formula and projection theorems ( Theorems 4.9, 4.10, 4.11) 
-Review problems:
4.1 #  10, 25, 27 
4.3 #  10a, 16, 19, 30a, 32, 
4.4 # 2, 8, 10, 13, 23. 
4.5 # 2a, 13a, 20, 29
Chapter Review-page 286
 True or False 1-12
 
 CHAPTER 6  Determinants. Section 1-5
-Determinants, Cofactor  Expansion
-Properties of determinants 
-determinants and matrix operations  
-Inverse of a matrix using cofactors, Theorem on page 388.  
-Cramers's Rule 
-Review problems:
6.1 # 8, 12, 14. 
6.2 #  7c,8, 9, 14, 16, 17, 24, 26a, 30 
6.3 # 3ab, 12. 
6.4 # 2, 11 
6.5 #1, 3, 8
Chapter Review-page 391
 True or False 1-7, 
Quiz (page 392) 1, 2, 4, 5, 7, 8

CHAPTER 7  EIGENVALUES and EIGENVECTORS: Section 1
-eigenvalues, eigenvectors, eigenspaces of a matrix
- Know to find the characteristic polynomial, the  characteristic equation and
  bases for eigenspaces of a  matrix.
 -eigenvalues of a triangular matrix. 

-Review problems:
7.1 # 5abc, 7, 9bd, 17, 21, 22, 24ab.