Matrices are defined as rectangular arrangement of numbers. The numbers in the metrices are called elements. They are arranged in rows and columns. Each matrix is arranged with the same number of rows and columns. The main focus of matrices is to represent linear transformation. Matrices are applied in the scientific fields like mechanics, electromagnetism, quantum mechanics etc. They are also used in economics. Matrices simplify calculations both in theory and practicals. This is a very important chapter in maths for 12th standard students of CBSE Board. Solutions to all the questions in this chapter can be easily found in any good solution key that provides NCERT Solutions for Class 12 Maths. Matrices can be used for real numbers or complex numbers. Matrices consist of numbers, symbols or expressions. The horizontal lines of elements are called as constitute row of matrix and the vertical lines of elements are called as constitute columns of matrix.
Order of Matrix
A matrix consists of m rows and n columns is called matrix of order. For example, m x n matrix.
The formula of matrix is, A = [aij]m × n
Size of the matrices
Depending on the number of rows and columns the size of the matrices are defined. A matrix with m x n where m is number of rows and n is number of columns known as dimensions. Matrices consisting of single row are called as row vectors and single column are called as column vectors.
Types of matrices
1. Row matrix: consist of only one row
2. Column matrix: consist of only two column
3. Square matrix: number of rows are equal to the number of columns
4. Diagonal matrix: if all the non diagonal elements are zero
5. Scalar matrix: if diagonal elements are equal
6. Identity matrix: a square matrix in which elements in the diagonal are all 1 and rest are zero.
7. Zero matrix: if all the elements are zero
Addition of matrices :If they are of the same order then matrices can be added.
Multiplication of matrices: If the number of columns is equal to the number of rows then it can be multiplied.
Transpose matrix: If A = [aij] be m x n matrix, then the matrix is obtained by interchanging the rows and columns of A is known as transpose of A. It is denoted by A′ or (AT). Submatrices are the matrices obtained by deleting collection of rows and columns.
Applications
- Probability theory and statistics
- Linear combinations of quantum states
- Electronics
- Geometrical optics
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