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Triangular Matrix

There are two types of triangular matrices.

1. Upper Triangular Matrix: A square matrix (aij) is said to be an upper triangular matrix if all the elements below the principal diagonal are zero (0). That is, [aij]m × n is an upper triangular matrix if (i) m = n and (ii) aij = 0 for i > j.


Examples of an Upper Triangular Matrix are:

(i) [5280310008]

(ii) [173061005]


(iii) [303071002]


2. Lower Triangular Matrix: A square matrix (aij) is said to be a lower triangular matrix if all the elements above the principal diagonal are zero (0). That is, [aij]m × n is a lower triangular matrix if (i) m = n and (ii) aij = 0 for i < j.

Examples of a Lower Triangular Matrix are:

(i) [700390121]


(ii) [100510371]


(iii) [900130254]


Definition of Triangular Matrix:

A square matrix is said to be a triangular matrix if it is either upper triangular or lower triangular.

For example:

(i) [231013004]


(ii) [100230412]


(iii) [000300210]


(iv) [012003000]


A diagonal matrix is both upper triangular and lower triangular.





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