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Find an LU factorization of the matrices in Exercises $7-16$ (with $L$ unit lower triangular). Note that MATLAB will usually produce a permuted LU factorization because it uses partial pivoting for numerical accuracy.$$\left[\begin{array}{rrr}{3} & {-6} & {3} \\ {6} & {-7} & {2} \\ {-1} & {7} & {0}\end{array}\right]$$

Hence $A=L U=\left[\begin{array}{rrr}{1} & {0} & {0} \\ {2} & {1} & {0} \\ {-1 / 3} & {1} & {1}\end{array}\right]\left[\begin{array}{ccc}{3} & {-6} & {3} \\ {0} & {5} & {-4} \\ {0} & {0} & {5}\end{array}\right]$

Algebra

Chapter 2

Matrix Algebra

Section 5

Matrix Factorizations

Introduction to Matrices

Missouri State University

Oregon State University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

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04:20

Find an LU factorization o…

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06:49

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03:28

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Determine the LU factoriza…

were given a matrix and were asked to find an L U factory ization for this matrix with L Unit Lower Triangular Matrix is a three by three matrix with entries three negative 63 six Negative seven to negative 170 First, let's roll birdies a using Onley row replacement operations. So first I'm going to subtract to over one from Road to. So I obtained three negative 63 zero five negative four and then I'm going to add one third of Rohan to Row three. So I get zero five one and next I'm going Thio. Subtract two. Wrote to from Road three to get three negative six three 05 Negative four zero zero five and this is going to be the row echelon matrix you and to obtain l first Pivot column was 36 negative one. Dividing by the pivot, which is three. We obtained that the first column novel is one to negative one half or, I mean negative. One third. Second pivot column is 55 dividing by the pivot, which is five. We get 011 and third Pivot column is five, divided by the pivot, which is five we obtained 00 one. So this is our matrix l And we have that a could be factored as l times you.

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