7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8...

A = (a_1 b_1 c_1 0 b_2 c_2 0 0 c_3) and B = [x_1 y_1 z_1 0 y_2 z_2 0 0 z_3] Both are Lower triangular matrix, Now order to find A B we have AB = [a_1 b_1 0 b_2 c_2 0 0 c_3] [x_1 y_1 z_1 0 y_2 z_2 0 0 z_3] [a_1 x_1 + 0 + 0 b_1 x_1 + b_2 y_1 + 0 c_1 x_1 + c_2 y_1 + c_3 z_1 0 + 0 + 0 0 + b_2 y_2 + 0 0 + c_2 y_2 + c_3 z_2 0 + 0 + 0 0 + 0 + 0 0 + 0 + c_3 z_3] (a_1 x_1 b_1 x_1 + b_2 y_1 c_1 x_1 + c_2 y_2 + c_3 z_1 0 b_2 y_2 c_2 y_2 + c_3 z_3 0 0 c_3 - z_3)_3 times 3 which is the Lower triangular matrix