MATRICES
TYPES OF MATRICES
ORDER OF A MATRIX
EQUALITY OF MATRICES
Form - x,y = row,column
2x2
1x3
Diagonal Matrix
Scalar Matrix
Square Matrix
Identity Matrix
Row Matrix
Column Matrix
Has only 1 column.
Has only 1 row.
Has equal number of rows and columns.
Has non-diagonal elements equal to 0.
Has non-diagonal elements equal to 0 and diagonal elements are same.
Has non-diagonal elements equal to 0 and diagonal elements are equal to 1.
Zero Matrix
Has all elements equal to 0 irrespective of the order.
Each element of all the given matrices should be equal to each other.
The order of the given number of matrices should be same.
OPERATIONS OF MATRICES
Addition of matrices
Commutative law
Associative law
Existence of additive identity
Existence of additive inverse
Scalar multiplication of matrix
Multiplication of matrices
Existence of multiplicative identity
Distributive law
Associative law
TRANSPOSE OF A MATRIX
(kA)' = kA' (where k is any constant)
(A + B)' = A' + B'
(A')' = A
(A B)' = B' A'
SYMMETRIC AND SKEW SYMMETRIC MATRIX
Symmetric Matrix
Skew Symmetric Matrix
A' = A
A' = - A
All the diagonal elements of the matrix are zero.
ELEMENTARY OPERATION (TRANSFORMATION) OF A MATRIX
The multiplication of the elements of any row or column by a non-zero number.
The addition to the elements of any row or column, the corresponding elements of any other row or column multiplied by any non-zero number.
The interchange of any two rows or two columns.
INVERTIBLE MATRICES
AB = BA = I
B is the inverse of A.
A is the inverse of B.
INVERSE OF A MATRIX BY ELEMENTARY OPERATIONS