Review for MIDTERM EXAM I (Tuesday, October 18).

CHAPTER 1,  Linear Equations and Matrices: Sections 1.2 - 1.6 
-Matrix operations: properties, powers of a matrix. 
-Special type of matrices: symmetric, skew symmetric, identity matrix, 
       partitioned  matrices.  
-Nonsingular (invertible) matrices: properties.
-Linear systems and inverses.
-Matrix transformation
Review problems:
1.2 #  2,  8, 10, 11. 
1.3 # 10, 22, 30, 41, 43.
1.4 #  8, 10,  32, 36 
1.5 #  9, 12, 15, 18,  31, 32, 44.  
1.6 # 12,16, 18, 19.

CHAPTER 2, Solving  Linear Systems: Section 2.1 and  Section 2.2  
-(REF)  and Gauss Elimination Method 
-(RREF) and Gauss- Jordan Method
-Finding the inverse of a matrix 
-Characterize Nonsingular matrices (Result on page 104) 
Review problems:
2.1 #  6, 7, 14, 22,  33. 
2.2 # 8, 9, 10ab, 16, 18, 19, 20, 28, 30.
 

CHAPTER 9, Real  Vector Space. Sections: 3.2-3.5 and Section 3.7
-Vector Space: definition, properties
-Subspace: definition, span, null space of a matrix. 
-Span and Linear dependence/ independence.
-Basis and Dimension
-Vector spaces of dimension n: properties, know how to find bases. 
-Coordinates and isomorphism: transition matrices. 
Review problems:
3.2 #  2, 17, 20.
3.3 #  4, 6, 8, 12bc, 14, 15, 28ab. 
3.4 # 2a, 4a, 8, 15b, 16, 20, 22, 24.
3. 5 # 2bc, 4b, 8a, 12, 18, 20b, 24b, 26bc, 28b, 30, 34. 
3.7 # 4, 10, 13abc, 14abc, 22, 24.