3) Finol a sequence of ele mentary materces, that canbe used to Iwrite the matrit in-echelonfarm.cow-3.4-4-54101 224

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Description: 3) Finol a sequence of ele mentary materces, that canbe used to Iwrite the matrit in-echelonfarm.cow-3.4-4-54101 224

The given matrix 010312-4-424-54. The elementary matrices are obtained as follows: MatrixElementary…

Answered: Find a sequence of elementary mateices,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3) Finol a sequence of ele mentary materces, that can
be used to Iwrite the matrit in
-echelon
farm.
cow-
3.
4-4
-54
10
1 2
24

Expert Solution

Step 1

The given matrix $[\begin{matrix} 0 & 1 & 0 & 3 \\ 1 & 2 & - 4 & - 4 \\ 2 & 4 & - 5 & 4 \end{matrix}]$ .

The elementary matrices are obtained as follows:

$\begin{matrix} M a t r i x & E l e m e n t a r y r o w o p e r a t i o n & E l e m e n t a r y M a t r i x \\ [\begin{matrix} 1 & 2 & - 4 & - 4 \\ 0 & 1 & 0 & 3 \\ 2 & 4 & - 5 & 4 \end{matrix}] & R_{1} \leftrightarrow R_{2} & [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}] \\ [\begin{matrix} 1 & 2 & - 4 & - 4 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 3 & 12 \end{matrix}] & R_{3} \to R_{3} - 2 R_{1} & [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & - 2 & 1 \end{matrix}] \\ [\begin{matrix} 1 & 2 & - 4 & - 4 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & 4 \end{matrix}] & R_{3} \to \frac{1}{3} R_{3} & [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & - \frac{2}{3} & \frac{1}{3} \end{matrix}] \\ [\begin{matrix} 1 & 0 & - 4 & 10 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & 4 \end{matrix}] & R_{1} \to R_{1} - 2 R_{2} & [\begin{matrix} - 2 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & - \frac{2}{3} & \frac{1}{3} \end{matrix}] \\ [\begin{matrix} 1 & 0 & 0 & 6 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & 4 \end{matrix}] & R_{1} \to R_{1} + 4 R_{3} & [\begin{matrix} - 2 & - \frac{5}{3} & \frac{4}{3} \\ 1 & 0 & 0 \\ 0 & - \frac{2}{3} & \frac{1}{3} \end{matrix}] \end{matrix}$

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