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 -#--##-
7.
8.
9.
10. You can add or subtract
matrices to get new
information.
You must have matrices
with equal dimensions.
You will combine
corresponding elements.
11.
12.
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
21. Since the two matrices
are equal, their
corresponding elements
are equal.
Set up equations using
corresponding elements
Solve for the variable
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