Question

Sum of an upper triangular matrix and lower triangular matrix can result in a triangular matrix.

• A. True
• B. False

Answer 1

The correct option is A

True

For proving this we need only one case for which the statement is true since the question contains the phrase “can result”.

We know that a diagonal matrix is also a triangular matrix. If we add two diagonal matrices we get a diagonal matrix which again is a triangular matrix. This proves the original statement. Hence the given statement is true. The answer would have been false if the question statement was "Sum of an upper triangular matrix and lower triangular matrix always results in a triangular matrix."