Transcript Welcome to Matrix Multiplication

Welcome to the world of Matrices
Sections 4-1 and 4-2
How do we define a matrix?
• A matrix is a rectangular
array of numbers written
within a bracket.
• A matrix is represented by
a capital letter.
• A matrix is classified first by
the number of rows and
then by the number of
columns in the matrix.
Let’s look at a few examples
This matrix has 2 rows and 1
column so its dimension is a
2x1
This matrix has 1 row and 3
columns so its dimension is a
1x3
This matrix has 3 rows and 3
columns so its dimension is a
3x3
Each number in a matrix is a
matrix element
You can identify a matrix element by its
position in the matrix
Use a lower case letter with a subscript to
represent the matrix element’s row
number and column number
The lower case letter corresponds to the
name of the matrix and the subscript
represent the row and column in which
the number appears.
Let’s look at some examples
A=
the first element is a11 = 2
the second element is a21 = 1
B=
b11 = 7, b12 = 4, b13 = 2
c11 =
c23 =
c13 =
c3 2=
c21 =
c1 2=
C=
We can only add or subtract matrices that
have the same dimensions
+
We can add these matrices because they
have the exact same dimensions All we
do is add corresponding elements and
put the answers into a new matrix with the
same dimensions.
4+2 =6
17 +1 = 18
The new matrix is
Now for the fun stuff…doing
the actual addition and
subtraction
Another example…