Transcript Intro to Matrices 6.1

Matrices
Today is a big notes day, we have
to get the foundation so that we
can start expanding on the basics.
Definitions…..
A Matrix is a rectangular array of
numbers, symbols, or variables. The
individual items in a matrix are
called its elements. It is enclosed
with brackets.
A matrix looks like
this.
Dimension - number of rows by number of
columns of a matrix.
**A matrix is named by its dimensions
This is a 2x4 matrix.
Examples: Find the dimensions of
each matrix.
1 
2

1. A = 0

4
1

5 
8 

Dimensions: 3x2
2 


2. B =
3 
 
4 
Dimensions: 4x1
Special Matrices
• Column Matrix - a matrix with
only one column.
• Row Matrix - a matrix with only
one row.
• Square Matrix - a matrix that
has the same number of rows and
columns.
Two matrices are Equal if they have
the same dimension and each element
in one matrix corresponds to the same
element of the other matrix.
*The definition of equal matrices can
be used to find values when elements of
the matrices are algebraic expressions.
Example
Example 1: Solve for variables
 2x  y  * Since the matrices are
1. 
   equal, the corresponding

2x  3y  12  elements are equal!
* Form two linear equations.
2x  y
2x  3y  12
* Solve the system using
substitution.
2x  y
y  3y  12
4y  12
y3
2x  3
3
x
2
Example 2: You try!
3x  y  x  3
2. 
 


x  2y  y  2 
Steps:
1. Write 2 linear equations.
2. Combine like terms.
3. Solve system using elimination.
3x  y  x  3
2. 
 


x

2y
y

2

 

3x  y  x  3
x  2y  y  2
* Write as linear equations.
* Combine like terms.
* Solve using elimination.
2x  y  3
2x  y  3
x  3y  2
2x  1  3
2x  2
x 1
Now check your answer
x  2y  y  2
1  21  1 2
1  2  1
1  1
2x  6y  4
7y  7
y1
Example 3: you try!
2x
3 3z  5 3y 9
Set each element equal and solve!
2x  5
5
x
2
3  3y
y1
3z  9
z 3
Jim, Mario and Mike are married to Shana, Kelly and
Lisa. Mario is Kelly’s brother and lives in Florida
with his wife. Mike is shorter than Lisa’s husband.
Mike works at a bank. Shana and her husband live in
Kentucky. Kelly and her husband work in a candy
store. Who is married to whom?
Jim
Mario
Mike
Shana
X
X
√
Kelly
√
X
X
√
X
X
Lisa