# Triangular matrix

If **U _{1}**,

**U**are upper triangular and

_{2}**L**,

_{1}**L**are lower triangular, which of the following are triangular?

_{2}- U1 + U2
- U1U2
- U1
^{2} - U1 + L1
- U1L1
- L1 + L2

If U1, U2 are upper triangular and L1, L2 are lower triangular, which of the following are triangular?
U1 + U2
U1U2
U12
U1 + L1
U1L1
L1 + L2

Kishor
Kumarhi.friend_zone@rocketmail.comSubscriberSOLVE - ΜΔΓΗŠ
Part 1 of solution

Part 2 of solution

The solution/proof is attached below.

Conclusion:

(U1+U2), (U1*U2), U1^2 & (L1+L2) are always Triangular Matrices (first 3 matrices – Upper Triangular & last matrix – Lower Triangular) if all of these operations can be done.

(U1+L1) & U1L1 can be a triangular matrix only if both U1 & L1 are diagonal matrices (i.e. both upper & lower triangular matrices) of the same order. Otherwise, they are not triangular matrices.