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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.$$\left[\begin{array}{rr}{2} & {5} \\ {-3} & {-4}\end{array}\right]$$

$L=\left[\begin{array}{rr}{1} & {0} \\ {-3 / 2} & {1}\end{array}\right], U=\left[\begin{array}{cc}{2} & {5} \\ {0} & {3.5}\end{array}\right]$

Algebra

Chapter 2

Matrix Algebra

Section 5

Matrix Factorizations

Introduction to Matrices

King R.

March 31, 2021

Im still confused how you got U.

Oregon State University

Harvey Mudd College

Baylor University

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given the Matrix and were asked to find an l U factory ization of the Matrix, where Elyse Unit Lower Triangular Matrix matrix were given is 25 negative three negative four. I'll call this Matrix a Now we see that this could be row reduced to 2507 halves, which we see this is going to be are row echelon matrix you So two by two matrix are triangular matrix. L is really going to be a two by two matrix and we we obtain it is we're going to take first the first pivot column A. So we have to negative three. And we're going to divide the column by the pivot, which is to So you're dividing by two. We put this into l is our first column. We get the l is one negative three halves, The first column and then we're going to add three halves times. Real Wonder wrote to so mhm. We have seven halves from you. We're going to divide this by seven halves, of course, so that we get 01 for our second column and so follows the metrics. L is 10 negative. Three halves one and the matrix you is 2007 Hats

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