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 [aij]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.
is a column matrix having one column and three rows.
are column matrices since they have only one column.
In general [aij]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.
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 a11, a22, a33, a44,…….., ann are known as diagonal elements.
In the matrix
3, 7, 0 are diagonal elements.
Diagonal matrix: A square matrix A= [aij]n×n is said to be a diagonal matrix if all its non
diagonal elements are zero ie aij = 0 if i ≠ j.
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.
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 In where n is ordered.
Null Matrix or Zero Matrix: A matrix in which all the elements are zero.
We denote this matrix by O.
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