# Math 544, Exam 1 Information

## Exam1 will be based on:

• Sections1.1 - 1.3,1.5 - 1.7,and 1.9.

• The corresponding assigned homework problems

**At minimum, you**

need to understand how to do the homework problems.

need to understand how to do the homework problems.

• Lecture notes: 1/17- 2/12.

## Topic List(not necessarily comprehensive):

**You will need to know how to define vocabulary words/phrases defined in class.**

§

**1.1**: Matrix representation of a linear system: coefficient matrix, augmented matrix, ele-

mentary row operations ,row equivalence.

§

**1.2**: Solving linear systems via

**Gauss- Jordan elimination :**echelon and reduced echelon

forms of a matrix, identifying dependent and independent variables , recoginizing when a

system is consistent /inconsistent.

§

**1.3**: Relationship between # nonzero rows and # columns in an augmented matrix in re-

duced echelon form. Homogeneous linear systems . # possible solutions to

1. a general linear system .

2. an m×n system with m < n.

3. a homogeneous system .

§

**1.5**: Matrix operations: addition, multiplication, multiplication by scalars, scalar (dot)

product in .

§

**1.6**: Properties of matrix addition,multiplication,and multiplication by scalars. The matrix

transpose and its properties ,scalar (dot) product and its relation to vector norm (length).

§

**1.7**: Linear combinations, linear dependence/independence: determinination of whether a

given set of vectors is linearly dependent /independent. Non-singular matrices; conditions

equivalent to non -singularity of A ∈ Mat

_{n×n}:

1. Ax=θ has only the trivial solution x =θ

2. columns of A are linearly independent

3. , Ax b has a unique solution .

4. A is invertible.

5. A is row equivalent to the identity ,I

_{n}.

§

**1.9**: Matrix inverses: existence of inverses (see above,e.g.,A is invertible A is non-

singular),using inverses to solve systems ,computing inverses by row reduction ,formula for

inverse of 2 ×2; matrix, algebraic properties .

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