Let U and R be nn upper triangular matrices and set T = UR. Show that T is also upper triangular and that t j j = u j jr j j for j = 1, . . . , n. 1

Matrix and Vector Multiplication Wednesday, October 12, 2016 4:03 PM Multiplying a Matrix and a Vector Let a1… am, and x be vectorsin Rn Example: Theorem: Let a 1 a m and b be vectorsin R n 1. b is in the span(1 , … ,mu ) 2. b = ▯▯ ▯▯ + ▯▯ ▯ + ⋯+ ▯ ▯▯ ▯▯ ℎas at least one solution 3. Linear system of [u 1 u2, …, m , b] has at least one solution 4. This: has at...