Exam 2 Guide, Professor Leibowitz’s Mathematics 2210 classes
I. Scope of the examination.
The material in these sections in our textbook forms the basis of Exam 2:
•1.9 The Matrix of a Linear Transformation
•2.1 Matrix Algebra
•2.2 Inverse of a Square Matrix
•2.3 Characterizations of Invertibility for a Square Matrix
•2.5 The LU Factorization
•3.1 The Determinant of a Square Matrix
•3.2 Properties of Determinants
II. Exam Problems
A. Calculations
•Find the matrix of a given linear transformation from Rnto Rm.
•Find the inverse of a matrix using row operations.
•Find an A=LU factorization, then use it to solve a system of equations.
•Calculate a determinant.
B. Theory
•One to one, onto.
•Solution of Ax=bwhen Ais invertible.
•Apply the Invertible Matrix Theorem and its Chapter 3 extensions.
•A number of True/False questions about the theory of matrices.
•Properties of determinants.
These topics will will not be examined : Partitioned Matrices, Cramer’s Rule, Determinants
and Volume.
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