Review for MIDTERM EXAM II (Thursday -November 4).

REVIEW the Homework problems of HW #4 and Hw #5 
(INCLUDING the ``prepare for the quiz''ones)

CHAPTER 3, MATRICES (Section 3.3, 3.5  and Section 3.6)
-Know how to find the inverse of a 2 by 2 or 3 by 3 matrix.
-subspaces,  basis,  dimension
-know to find bases for the row space, the column space 
  and the  null space of a matrix
-rank, Rank Theorem
-FTIM (version 1 & 2)
-coordinate of a vector with respect to a basis
Section  6
-Linear transformations
-The matrix associated with a linear transformation
-Composition of linear transformations
 
Extra problems:
Section 3.3 # 47, 49, 53
Section 3.5 # 55, 56, 58, 63
Section 3.6 # 23, 36, 39

 CHAPTER 4  EIGENVALUES and EIGENVECTORS - (Section 1 & Section 2)
Section 1
-Definitions for eigenvalues, eigenvectors, eigenspaces of a matrix
-Know how to find  eigenvalues, eigenvectors, eigenspaces for a 2 by 2 matrix
Section 2
-Determinants, (Laplace) Expansion Theorem
-Properties of Determinants 
(from section 4.2: Theorem 2, 3, 6, 7, 8, 9, 10)
-The  formula for the inverse of a matrix  (Theorem 12)
-Cramers's Rule 

Extra problems:
Section 4.1 # 25, 35, 37

Review problems for Section 4.2:
Section 4.2 # 1, 3, 7, 9, 17, 25, 35, 39, 49, 53, 55
Section 4.2 # 4, 8, 12, 14, 26, 28, 36, 38, 40, 46, 50, 52, 54, 56, 58 6