Reduced Row EchelonForm

Matrices and the Calculator

Matrix Solution of Systems by Calculator

Write the system of equations as an augmented matrix

5 7 9

3 11 6

x y

x y

2 3

5 7 9

3 11 6

EDIT

Input data

Menu 1

Matrix Solution of Systems by Calculator

Menu B:rref(

So the solution to

5 7 9

3 11 6

57 3is , .

34 34

x y

x y

Menu 1

Menu 1

Example Solve the system:

2 4 3

4 5

6 2 10

x y z

x z

x y z

Solution In solving systems of equations, we perform computations with the constants. The variables play no important role until the end, so why not use an augmented matrix.

Augmented Matrix

3 4 matrix

rref

The solution to this system is (3, 7, -1/2).

2 1 4 3

1 0 4 5

6 1 2 10

2 1 4 3

1 0 4 5

6 1 2 10

1 0 0 3

0 1 0 7

10 0 1 2

2 4 3

4 5

6 2 10

x y z

x z

x y z

Standard Form

Examples Use matrices and your calculator to solve the system.

2 8

1

2 2

x y z

x y z

x y z

2 8 2 4

6 3 4

3 2 0

x y z

x y z

x y z

2.12 1.18 12.76 7.49

0.17 6.52 3.09 11.34

3.06 2.89 0.81

x y z

x y z

x y z