Review for MIDTERM EXAM I(Thursday-September 30).

Review the Homework problems.

CHAPTER 1- VECTORS (Section 1.1, Section 1.2)

-Geometry and algebra of vectors.
-Triangle rule and parallelogram rule.
-Linear combinations of vectors.
-Dot product, the angle between two vectors, norm.
-Orthogonal vectors, projection of a vector onto another vector.
-Review problems:
 1.1 # 14, 18, 19
 1.2 # 20, 26, 28,37, 48, 56, 60, 66.

CHAPTER 2 SYSTEMS - (Sections 2.1-2.3)

-Consistent (inconsistent) systems. 
-Augmented matrix.
-Row echelon form - Gaussian Elimination
-Reduced row echelon form- Gauss-Jordan Elimination.
-The rank Theorem.
-Homogeneous systems.
-Span, spanning sets.
-Linearly dependent/independent vectors and
 the connection with homogeneous systems theory.
-Review problems:
 2.1 # 22, 24 26, 38
 2.2 # 8, 14, 24, 26, 28, 36, 38, 41, 42.
 2.3 # 3, 8, 12, 10, 20, 24, 28, 34, 42, 43,  44, 46, 48


CHAPTER 3 MATRICES (Sections 3.1-3.3)

-Operations with matrices (properties).
-The transpose of a matrix (properties).
-The inverse of a matrix (properties).
-Symmetric matrices, properties. 
-Know how to find the inverse of a 2 by 2 matrix.
-Review problems: 
 3.1 # 12, 13, 29, 34, 36, 37, 38
 3.2 # 1, 3, 22, 23, 27, 35, 44, 45, 47
 3.3 # 3, 4, 9, 12, 17, 21, 22, 33, 42, 44, 45, 46, 64, 6