matrices: simplifying algebraic expressions combining like terms & distributive property
TRANSCRIPT
Matrices: Simplifying Algebraic Expressions
Combining Like Terms & Distributive Property
Matrix
Rectangular arrangement of numbers into rows and columns.
65
43
Matrix
Row: horizontal arrangement of numbers
Column: vertical arrangement of numbers
This matrix has 3 rows
and two columns.
k
n
m
v
y
x
10
9
4
6
5
3
Matrix Vocabulary
The plural form of matrix is matrices.
The numbers in a matrix are called elements or entries.
A matrix that has the same number of rows as columns is called a square matrix.
Dimension of a matrix
Dimension is determined by:
Row x Column
This matrix has a dimension of 2 x 3 or 2 by 3.
z
y
b
a
y
x
10
8
4
3
5
6
Operations with Matrices
To add or subtract matrices, matrices must have the same dimensions.
To add or subtract matrices, add or subtract corresponding entries to form one matrix.
Corresponding entries have the same row number and the same column number.
Operations with Matrices
Examples:
1. [A] + [B] 2. [A] – [B] 3. [B] – [A]
0
20
25
15A
15
6
25
10B
Operations with Matrices
Example:
4. [C] + [D] 5. [C] – [D]
n
m
j
h
y
xC
15
5
10
7
5
3
n
m
j
h
y
xD
8
5
21
11
6
8
Scalar Multiplication
Scalar Multiplication: multiplication of a matrix by a real number.
To multiply a matrix by a scalar, multiply each entry by the real number to form a new matrix.
Real numbers are sometimes called scalars.
Scalar Multiplication
Example:
6. 9[E] 7. –3[F]
)5(
)35(
)42(
)2(
m
y
n
xE
)6(
)32(
)42(
)6(
m
y
k
wF
Let’s Practice!
Complete page 28, problems 38-41.Complete page 35, problems 56-58.Complete page 43, problems 90-95.
NO CALCULATOR!