3.1 Systems of Two Linear Equations in Two Variables

A. Solve the system by graphing (by hand or with Excel)

3x +5y = 46

7x – y = 6

B. Solve the system by graphing (by hand or with Excel)

4x – 5y = 7

2x + 3y = 9

3.2 Matrices and Linear Equations in Two Variables

C. Find the dimensions of the matrix and the values of a2,1 and a3,1

5 9 1 2

3 6 12 4

2 7 3 8

D. Find the dimensions of the matrix and the values of a1,3 and a2,3

7 5 3 4

9 1 14 2

8 6 9 10

E. Write the augmented matrix representing the system of linear equations.

5 7 2

2 3

x y

x y

F. Write the augmented matrix representing the system of linear equations.

3 5 8

4 5

x y

x y

G. Carry out the row operation:

2 2

1 1 12 32

2 0 2 16

R R

H. Carry out the row operation:

1 1

1 8 24 32

8 5 22 16

R R

I. Interpret the augmented matrix as the solution of a system of equations. State the solution, or identify the system as

inconsistent or dependent.

1 0 9

0 1 15

MAT230 – Finite Analysis

Unit 3 DB: Systems of Equations and Matrices

J. Interpret the augmented matrix as the solution of a system of equations. State the solution, or identify the system as

inconsistent or dependent.

1 0 157

0 1 386

K. Solve the system by row-reducing the corresponding augmented matrix.

2 12

3 11

x y

x y

3.3 Systems of Linear Equations and the Gauss-Jordan Method

L. Find the augmented matrix representing the system of equations:

1 2 3

1 2 3

1 2

2 2

3 4 6

3 1

x x x

x x x

x x x

M. Interpret the row-reduced matrix as the solution of a system of equations:

1 0 0 5

0 1 0 9

0 0 1 2

N. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix:

1 0 1 15

0 1 0 9

0 0 1 2

O. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix:

1 0 0 7

0 1 0 16

0 0 2 32

3.4 Matrix Arithmetic

For problems P – U, use matrices A, B, and C below.

2 3 4 8 7 6 1 6 5

5 6 7 5 4 3 7 2 8

8 9 1 2 1 9 4 9 3

A B C

P. Find: A

t

Q. Find: 2B

R. Find: –3C

S. Find: B + C

T. Find: C – A

U. Find: A + 2B

V. Find the matrix product:

2

2 3 1

1

3 1 3

2

W. Find the matrix product:

2 2

2 3 1

1 4

3 1 3

3 3

X. Find the matrix product:

2

4 5 2

3

1 1 3

2

Y. Rewrite the system of linear equations as a matrix equation AX = B

1 2 3

1 2 3

1 2 3

2 3 4 1

5 8 6 3

2 3 3 8

x x x

x x x

x x x

Z. Rewrite the system of linear equations as a matrix equation AX = B

1 2 3 4

1 2 3 4

1 2 3 4

2 3 4 5 6

5 8 6 4 1

2 3 3 6 14

Sample Solution