Exercise23.6

Recall the definition of a lower triangular and unit lower triangular matrices in Exercise 2.6. Also, an upper triangular matrix is one whose transpose is lower triangular. Let \(L_1\) and \(L_2\) be unit lower triangular matrices. Let \(U_1\) and \(U_2\) be nonsingular upper triangular matrices. Suppose that \(L_1U_1=L_2U_2\text{.}\) Show that \(L_1=L_2\) and \(U_1=U_2\text{.}\)