Question-14

Find the number of true statements. Your answer should be between \(0\) and \(4\):

• The product of two upper triangular matrices is upper triangular.
• The product of two lower triangular matrices is lower triangular.
• If \(L\) is an lower triangular matrix then \(L^T\) is lower triangular.
• If \(U\) is an upper triangular matrix then \(U^T\) is lower triangular.

Answer

\(3\)

Solution

The product of any two upper(lower) triangular matrices is upper(lower) triangular. An upper triangular matrix is the transpose of a lower triangular matrix and vice versa.