Math 202                                                                   C.S. Davis

Your are responsible for the subject matter in sections 2.1 - 2.5 from Elementary Linear Algebra, 5th edition, by Larson and Edwards. The following topics are the most important. Typical exercises are assigned at the end of each topic.  If you need more practice than these, work some more similar exercises.

2.1

1.

Give the basic definitions about matrices. Text

2.

Perform matrix arithmetic: matrix addition, subtraction, scalar multiplication and matrix multiplication.   P55#1,3,9,13

3.

System of linear equations can be written as a matrix equation and as equations involving linear combinations of columns. Given any of the three, convert to the other two. P59#61

4.

Solve a matrix equation using Gauss-Jordan method on the augmented matrix. P56#21,25,27

2.2

1.

Use and illustrate the properties of matrix arithmetic. P69#17,18,29

2.

Prove the properties of matrix arithmetic by using the definitions and the properties of real numbers. P70#45 and Text

3.

Use and illustrate the properties of transpose matrices. P70#23,29,33

4.

Prove the properties of transpose matrices by using the definitions and the properties of real numbers. P71#53 and Text

2.3

1.

Give the definition of inverse matrix and the theorem about the uniqueness of matrix inverses. Text

2.

Find A-1 by Gauss-Jordan elimination. (2 by 2, 3 by 3, etc.) P83#5,9,23

3.

Find A-1 by using the determinant. (2 by 2 only) P83#5

4.

Use and illustrate the 7 properties of inverses (from three theorems). P84#31

5.

State the existence and uniqueness theorem for solutions of systems of linear equations (theorem 2.11). Text

2.4

1.

Define elementary matrix. Text

2.

Determine whether a matrix is elementary and why. P95#1,3,5,7

3.

Find the elementary matrices whose product with a given matrix produces a matrix in row echelon form. P95#21,23,29,30

4.

Show that elementary matrices are invertible by finding their inverses. P95#13,15,17,19

5.

Give the equivalent conditions for invertibility. Text

6.

Determine whether a matrix is LU-factorable and perform LU-factorization. P96#37,39

7.

Solve an LU-factorable matrix equation, AX = B, i.e., LUX = B. P96#41

2.5

1.

Define stochastic matrix and matrix of transitional probabilities. Text

2.

Work consumer preference model applications. P110#1,7,9

3.

Work cryptography applications (encoding and decoding messages). P111#17

4.

Work Leontief input-output model application. P112#27,29