Transcript Notes Augmented Matrices

Augmented Matrices
I.. Matrix = an arrangement of #s in rows and columns.
A) Matrix: (plural is matrices). Symbol [
]
B) Order / Size of a matrix = (rows x columns)
1) number of rows
by # of columns
C) Entries = the numbers inside of a matrix.
D) Matrices are named with a capital letter.
E) Square matrix: # of rows = # of columns.
1) (2 x 2), (3 x 3), etc.
Augmented Matrices
II..Augment = to enhance, to make something bigger.
A) Augmented matrix = a linear system written as a single
matrix.
1) ax + by = #
a b #
a b #
cx + dy = #
Example:
3x + 4y = –6
2x – y = 7
c
d
3
2
#
or
4
–1
–6
7
c
d
#
Augmented Matrices
III..Solving Augmented Matrices with the N-spire
A)
B)
C)
D)
E)
Use black math icon
Menu 7 , 5 [Reduced Row-Echelon Form]
Menu 7 , 1
[Create]
Choose the size of your augmented matrix.
Type in the numbers
(use the “tab” button to jump to the next box)
F) Press ENTER to get your answer.
Example:
3x + 4y = –6
3 4
–6
1 0 2
2x – y = 7
2 –1
7
0 1 –3
The solution is (2 , –3)
Augmented Matrices on TI-84
I.. Entering a Matrix into the calculator.
1) Press
MATRIX
2) Go  to EDIT
(2nd Matrix)
(use scroll arrows)
3) Chose the desired matrix letter & press ENTER.
4) Use the scroll arrows to move the cursor.
Enter in the order / size of the matrix.
5) Type in the entries. Press enter after each one.
6) Press
2nd QUIT to exit the matrix screen.
Augmented Matrices on TI-84
III.. Using rref to Solve Systems of Equations.
A) Put the system into augmented matrix form.
1) Enter in the augmented matrix. (2x3) or (3x4)
2) Press
2nd QUIT to exit the matrix screen.
3) Press
MATRIX
(2nd Matrix)
4) Go  to Math and go down to “rref”. ENTER.
5) Press MATRIX & chose desired matrix.
6) Press ENTER to perform the math.