Properties of matrices
Addition, Multiplication, Determinants
1
A= 2
2
2
3
0
1
1
1
4
1
3
B=
D=
-3
E=
-4
1
G= 0
9
3X1
3
2
0
0
C=
-4
3X3
3X3
4 5
1 7
2X2
5
0
1
H=
1
0
0
2X2
4
2
1
0
2X3
0
1
0
3X3
1
-2
0
0
1
F=
4
-7
9
1X3
I=
1
6
7
4
3
1
3X2
Matrices
Let assume:
Then
Determinant of a matrix
The determinant of a matrix is a
scalar value that is used in many
matrix operations. The matrix
must be square (equal number of
columns and rows) to have a
determinant
2x2 and 3x3 matrix
The determinant of a 2×2 matrix is simply:
Properties of Addition
Let A, B and C be m x n matrices
1. A + B = B + A
commutative
2. A + (B + C) = (A + B) + C
associative
3. There is a unique m x n matrix O with
A+O = A
additive
identity
4. For any m x n matrix A there is an m x n matrix B
(called -A) with A + B = O
additive
inverse
Properties of Multiplication
Let A, B and C be matrices of dimensions such that the
following are defined. Then
1. A(BC) = (AB)C
associative
2. A(B + C) = AB + AC
distributive
3. (A + B)C = AC + BC
distributive
4. There are unique matrices Im and In with
Im A = A In = A
multiplicative identity