## Solution for problem 14 Chapter 1.5

# Let U and R be nn upper triangular matrices and set T = UR. Show that T is also upper

Linear Algebra with Applications | 8th Edition

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

**Accepted Solution**

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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 least one solution Linear Independence Thursday, October 13, 2016 12:07 PM Q: Given a set of vectors, when is one a linear combination of the others Let u1, … ,mu be vectorsin R . If the only solution▯ ▯▯ + ▯▯ ▯ + ⋯+ x ▯ ▯▯ Then the vectorsare said to be linearly independent. Otherwise linearly dependent. Example: Linear Independence Thursday, October 13, 2

###### Chapter 1.5, Problem 14 is Solved

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Let U and R be nn upper triangular matrices and set T = UR. Show that T is also upper