Matrices for Class 12: Matrices are one of the most powerful tools, which has various application such as in solving linear equations, in budgeting, sales projection, cost estimation, etc. Before going into the concepts let us know what are matrices.
A matrix is an ordered rectangular array of numbers or functions. These numbers or functions are known as the elements of the matrix.
Order of a matrix m × n, is defined as: ‘m’ number of horizontal rows and ‘n’ number of the vertical column.
Types of Matrices
Depending upon the order and elements, matrices are classified as,
A column matrix is an m × 1 matrix, consisting of a single column of m elements. It is also called a column vector.
A row matrix is a 1 × m matrix, consisting of a single row of m elements. It is also called a row vector.
A matrix which has an equal number of rows and columns. It is expressed as m × m.
A matrix which has non-zero elements in its diagonal part running from upper left to the lower right or vice versa.
The scalar matrix is a square matrix, which has all its diagonal elements equal and all the off-diagonal elements as zero.
A square matric which has all its principal diagonal elements as ones and all non-diagonal elements as zeros.
A matrix whose all entries are zero. It is also called a null matrix.
Equality of Matrices
Two matrices are said to be equal if-
(i) The order of both the matrices are the same
(ii) Each element of one matrix is equal to the corresponding element of the other matrix.