Download Matrices Basic Operations Notes Jan 25

Warm-UP
A= 7
9
C=
7
9
-8
-3
6
-4
7
8
10
-5
B=
-1
7
0
9
-3
-6
Find: A22 and C31
Find: the dimensions of each
Matrix
Find: A + B and B – A and C + B
Practice in Pairs
• When businesses deal with sales, there is a need to organize
information. For instance, let's say Karadimos King is a fast-food
restaurant that made the following number of sales:
• On Monday, Karadimos King sold 35 hamburgers, 50 sodas, and 45
fries. On Tuesday, it sold 120 sodas, 56 fries, and 43 hamburgers. On
Wednesday, it sold 15 fries, 12 hamburgers, and 19 sodas. Create a
matrix to hold this information.
Transpose Matrix: A matrix which is formed by
turning all the rows of a given matrix
into columns and vice-versa. The transpose of
matrix A is written AT.
1 4
1 2 3 T is
2 5
4 5 6
3 6
Equal Matrices: Two matrices are equal if they have
the same dimensions and the corresponding
elements are equal.
Multiplying a Matrix by a Scalar
•Multiply each element in the matrix by
the scalar to create a solution matrix.
•The solution matrix will have the same
dimensions as the original matrix.
Scalar Multiplication of Matrices
 2 8   4( 2 ) 4( 8 )   8 32 
4





 5 7   4( 5 ) 4( 7 )   20 28 
 15 12 10   3( 15 ) 3( 12 ) 3( 10 )   45 36 30 
3  10 20 0    3( 10 ) 3( 20 ) 3( 0 )    30 60 0 

 
 

 5
2 6   3( 5 )
3( 2 ) 3( 6 )   15 6 18 

Practice
7
-10
8
9
8
0
-3
-6
11
-4
=
Adding and Subtracting Matrices
•We can only add matrices of the same
order.
•Matrix addition and subtraction are very
simple; we just add or subtract the
corresponding elements.
•The solution matrix will have the same
order/dimensions.
Example
5
4
10
3
7
-2
-7
+
0
11
2
4
11
=
Example
5
4
10
3
7
-2
-7
-
11
4
0
2
11
=
Using Adding and Subtracting Matrices in Equations
ALGEBRA 2 LESSON 4-2
Solve X –
X –
X –
2 5
3 –1
8 0
+
2 5
3 –1
8 0
2 5
3 –1
8 0
2 5
3 –1
8 0
=
=
10 –3
–4 9
6 –9
=
10 –3
–4 9
6 –9
10 –3
–4 9
6 –9
+
for the matrix X.
2 5
3 –1
8 0
Add
2 5
3 –1
8 0
to each side of
the equation.
X =
12 2
–1 8
14 –9
4-2
Simplify.