The document defines matrices and matrix operations such as addition, subtraction and scalar multiplication. It provides examples of using matrices to organize data on students' wins and losses in a chess competition. It also discusses rules for matrix multiplication, including that the number of columns in the first matrix must equal the number of rows in the second matrix for the product to be defined. Examples are provided to illustrate solving systems of equations using matrix addition and multiplication.

2.  Matrix
 Matrix element
 Row
 Column
 Zero matrix
 Equal matrices
 Corresponding elements
 Scalar
 Scalar multiplication

3.  Rows x columns
 Read rows by columns
 Rows go across
 Columns go down
 [ 1 2 3 4 ] 1 x 4 matrix

4.  Element A 13
 Means the term in the 1st
row , 3rd column
 A
13 = 3

5.  Matrices can be used to
organize and compare
statistical data.

6.  Three students kept track
of the games they won
and lost in a chess
competition.
 # = won - = loss
 Ed # - # # - ##
 Jo ####-##
 Lou -#--##-

10.  You can add or subtract
matrices to get new
information.
 You must have matrices
with equal dimensions.
 You will combine
corresponding elements.

13.  MATRX
 Over 2 EDIT
 ENTER
 Put in the size of the matrix
 Remember rows x columns
 Press ENTER after each
element
 2nd QUIT

14.  Be sure to enter the
matrices into the
calculator as they are
given in the problem.

15.  Enter matrices as given in
the problem.
 2nd QUIT
 MATRX select Matrix A
 Then enter operation symbol
 MATRX select Matrix B
 ENTER, record the answer

16.  Same process as solving
linear equations
 Isolate the variable
 Use inverse operation
 Solve

17.  X - [ 1 1]= [0 1]
[ 3 2] [ 89]
Enter the 2nd matrix as A
since it is not going to
move.
Enter the 1 matrix as B.
st

18.  Same number of rows
 Same number of columns
 Corresponding elements
are equal

19.  [4] [3 4 7 ]
[6]
[8]
Equal matrices?
Why or why not?

20.  [ -2 3 ] [ -8/4
6-3 ]
[ 5 0] [ 15/3
4-4]
Equal matrices?
Why or why not?

21.  Since the two matrices
are equal, their
corresponding elements
are equal.
 Set up equations using
corresponding elements
 Solve for the variable

22.  [x+8 -5 ] = [ 38
-5 ]
[ 3 -y ] [3
4y-10]

23.  x + 8 = 38 -y = 4y –
10
 - 8 -8 -4y -4y
 x = 30 -5y =
-10
 y=2

24.  [ 3x 4] = [ -9 x
+y]

25.  Matrix multiplication is not
commutative.
 Order matters!

26.  Scalar is the number on
the outside of the matrix.
 Multiplying by a scalar is
just like distributive
property.

27.  Enter matrix into
calculator in matrix A.
 2nd QUIT
 Enter scalar, then choose
matrix A
 ENTER
 Record answer

28.  3[2 6]
[7 4]

29.  5A – 3B
 A + 6B
 5B – 4A

30.  Just like solving
equations with
distributive property
 To eliminate a scalar that
is a fraction….multiply by
the reciprocal

31.  -3y + 2 [ 6 9 ] = [ 27
-18 ]
[ -12 15] [ 30
6 ]

32.  2x = [ 4 12 ] + [ -2
0]
[ 1 -4] [ 3
4]

33.  -3x + [ 7 0 -1 ] = [ 10
0 8]
[2 -3 4] [-19
-18 10]

34.  Product exists only if
 The number of columns
of A
 EQUALS
 The number of rows of B

35.  Determine dimensions of each
matrix
 Determine dimension of product
matrix
 Check to see if # of Col. Of A
equals # of rows of B
 If yes = product defined
 If no = product undefined
 Undefined means does not exist.

36.  The number of rows of
matrix A
 By
 The number of columns
of matrix B

37.  If the number of columns
of A does not equal the
number of rows of B…..
 The calculator will give
you an error message.

38.  [ -2 5] [ 4 -4 ]
[3 -1] [2 6]
A has 2 rows and 2
columns.
B has 2 rows and 2
columns.
The col. Of A = the rows of

39.  [ 10 ] [ 12 3]
[ -5 ]
[1 2] [ 7 6 8 13 ]
[3 4] [ 9 10 11 19]

40.  [ w x ] [ 9 -7 ]
[ y z ] [3 1]
[ -3 5] [ -3 ]
[ 5]