Matrices – Matrix for Class 12 Mathematics Solutions

Order of a Matrix
There may be any number of rows and any number of columns in a matrix. If there are m rows and n columns in matrix A, its order is m x n and it is read as an m x n matrix.
Transpose of a Matrix
The transpose of a given matrix A is formed by interchanging its rows and columns and is denoted by A’.
Symmetric Matrix
A square matrix A is said to be a symmetric matrix if A’ = A.
Skew-Symmetric Matrix
A square matrix A is said to be a skew-symmetric if A’ = – A. all elements in the principal diagonal of a skew-symmetric matrix are zeroes.

Addition of Matrix
If A and B are any two given matrices of the same order, then their sum is defined to be a matrix C whose respective elements are the sum of the corresponding elements of the matrices A and B and we write this as C = A + B.

Types:
Row matrix: A row matrix has only one row but any number of columns.
Column matrix: A column matrix has only one column but any number of rows.
Square matrix: A square matrix has the number of columns equal to the number of rows.
Rectangular Matrix: A matrix is said to be a rectangular matrix if the number of rows is not equal to the number of columns.

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