## NCERT Solutions for class 12 Types of Matrices

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**Row matrix:** A matrix is said to be a row matrix if it has only one row.

Eg [ 1 5 2 ] _{1×3} is a matrix with one row and three columns. So, it is a row matrix.

[ 4 1/2 0 -3 ]_{1×4, } [ 1 0 ] _{1×3 }are row matrices since they have only one row.

In general [a_{ij}]_{1×n} is a row matrix of order 1×n.

**Column matrix: **A matrix is said to be a column matrix if it has only one column.

Eg .

is a column matrix having one column and three rows.

are column matrices since they have only one column.

In general [a_{ij}]_{m×1} is a column matrix of order m×1.

**Square matrix: **A matrix is said to be square matrix if the number of rows is equal to the number of columns. Thus, an m × n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘m’ or ‘n’.

*For the practice sets of Matrices & more, click on 12th Class Maths.*

Eg

is a matrix of order 2×2.Here m = n =2 and thus it is a square matrix.

are examples of square matrices.

In square matrices the entries a_{11,} a_{22,} a_{33,} a_{44,……..,} a_{nn} are known as diagonal elements.

In the matrix

3, 7, 0 are diagonal elements.

**Diagonal matrix: **A square matrix A= [a_{ij}]_{n×n } is said to be a diagonal matrix if all its non

diagonal elements are zero ie a_{ij} = 0 if i ≠ j.

Eg

All are diagonal matrices.

**Note: **There is no condition on the diagonal elements. They can be zero or non zero.

**Scalar matrix: **A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal or we can say that the nondiagonal elements are zero and the diagonal elements are equal.

Eg

**Identity Matrix: **A scalar matrix in which diagonal elements are only 1 ie nondiagonal elements are zero and rest are one. We denote this matrix by I_{n} where n is ordered.

**Null Matrix or Zero Matrix****:** A matrix in which all the elements are zero.

Eg

We denote this matrix by O.

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