Find an LU-factorization of the matrix. 12

Let A be the matrix -31120 Take the elementary matrix and multiply it with the matrix A to obtain…

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 13E

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Question

Find an LU-factorization of the matrix.

Transcribed Image Text:12

Expert Solution

Step 1

Let A be the matrix $[\begin{matrix} - 3 & 1 \\ 12 & 0 \end{matrix}]$

Take the elementary matrix and multiply it with the matrix A to obtain the upper triangular matrix U.

Apply the row operation $R_{2} \to R_{2} + 4 (R_{1})$ to reduce the matrix and obtain the elements of the elementary matrix. $A = [\begin{matrix} - 3 & 1 \\ 12 & 0 \end{matrix}] R_{2} \to R_{2} + 4 (R_{1}) E A = U [\begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}] [\begin{matrix} - 3 & 1 \\ 12 & 0 \end{matrix}] = [\begin{matrix} - 3 & 1 \\ 0 & 4 \end{matrix}]$

Thus the elementary matrix is $E = [\begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}]$

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