4.1 matrices
-
Upload
roiamah-basri -
Category
Education
-
view
740 -
download
0
Transcript of 4.1 matrices
11 12 13 14
21 22 23 24
31 32 33 34
mn mn mn mn
a a a a
a a a a
a a a a
a a a a
Row 1
Row 2
Row 3
Row m
Column 1 Column 2 Column 3 Column 4
A matrix of m rows and n columns is called a matrix with dimensions m x n.
2 3 41.) 1
12
π
− −
3 8 9
2.) 2 5
6 7 8
π− − −
103.)
7
−
[ ]4.) 3 4−
2 X 33 X 3
2 X 11 X 2
3 5
11.) 4
40π
− −
3 02.)
0 3
−
1 2 3
3.) 0 1 8
0 0 1
4.) 2π 5
5.)π−
[ ]6.) 3−
3 X 2 2 X 2 3 X 3
1 X 2 2 X 1 1 X 1
To add matrices, we add the corresponding elements. They must have the same dimensions.
5 0 6 3
4 1 2 3A B
− − = =
A + B5 6 0 3
4 2 1 3
− + + − = + +
1 3
6 4
− =
2 1 3 0 0 02.)
1 0 1 0 0 0
− + −
2 1 3
1 0 1
− = −
When a zero matrix is added to another matrix of the same dimension, that same matrix is obtained.
To subtract matrices, we subtract the corresponding elements. The matrices must have the same dimensions.
1 2 1 1
3.) 2 0 1 3
3 1 2 3
− − − − −
1 1 2 ( 1)
2 1 0 3
3 2 1 3
− − − − − − − − − −
0 3
3 3
5 4
= − − − −
4 1 6 51.)
6 3 7 3
− − − + −
1 3 2 2 1 52.)
4 0 5 6 4 3
− − − −
2 6
13 0
− − =
1 4 7
2 4 8
− − = − −
ADDITIVE INVERSE OF A MATRIX:
1 0 2
3 1 5A
= −
1 0 2
3 1 5A
− − − = − −
Find the additive inverse:
2 1 5
6 4 3
− −
2 1 5
6 4 3
− − = − −
Scalar Multiplication:
1 2 3
1 2 3
4 5 6
k
− − − −
We multiply each # inside our matrix by k.
1 2 3
1 2 3
4 5 6
k k k
k k k
k k k
= − − − −
3 01.) 3
4 5
−
9 0
12 15
− =
2
1 2
2.) 5 4 1
0 5
x
y
x
− − 2
5 10 5
20 5 5
0 25 5
x
y
x
− = −
=
−−
+
−812
026
2
14
58
132
y
x
=
−−+−+
812
026
528
11432
y
x
=
−
+812
026
56
0432
y
x
=
−
+812
026
21012
086
y
xScalar Multiplication:
6x+8=26
6x=18
x=3
10-2y=8
-2y=-2
y=1
• Associative Property of Addition(A+B)+C = A+(B+C)
• Commutative Property of AdditionA+B = B+A
• Distributive Property of Addition and Subtraction S(A+B) = SA+SB
S(A-B) = SA-SB• NOTE: Multiplication is not included!!!