. Find all the solutions in vector form of the following linear system using Gaussian eliminationT1- 712 + 624 = 513 - 214 =-z1 + 7r2 – 4r3 + 214 = 7.-3o Sunno0e thetnn follounılinoor cuotom heaougmontod metrin

Answered: Find all the solutions in vector form…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

. Find all the solutions in vector form of the following linear system using Gaussian elimination
T1- 712 + 624 = 5
13 - 214 =
-z1 + 7r2 – 4r3 + 214 = 7.
-3
o Sunno0e thet
nn follounı
linoor cuotom hea
ougmontod metrin

Expert Solution

Step 1

$g i v e n e q u a t i o n x_{1} - 7 x_{2} + 6 x_{4} = 5 x_{3} - 2 x_{4} = - 3 - x_{1} + 7 x_{2} - 4 x_{3} + 2 x_{4} = 7 [\begin{matrix} 1 & - 7 & 0 & 6 \\ 0 & 0 & 1 & - 2 \\ - 1 & 7 & - 4 & 2 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{matrix}] = [\begin{matrix} 5 \\ - 3 \\ 7 \end{matrix}] R_{3} \to R_{3} + R_{1} [\begin{matrix} 1 & - 7 & 0 & 6 \\ 0 & 0 & 1 & - 2 \\ 0 & 0 & - 4 & 8 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{matrix}] = [\begin{matrix} 5 \\ - 3 \\ 12 \end{matrix}] R_{3} \to R_{3} + 4 R_{2} [\begin{matrix} 1 & - 7 & 0 & 6 \\ 0 & 0 & 1 & - 2 \\ 0 & 0 & 0 & 0 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{matrix}] = [\begin{matrix} 5 \\ - 3 \\ 0 \end{matrix}] R_{1 \to} R_{1} + 3 R_{2} [\begin{matrix} 1 & - 7 & 3 & 0 \\ 0 & 0 & 1 & - 2 \\ 0 & 0 & 0 & 0 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{matrix}] = [\begin{matrix} - 4 \\ - 3 \\ 0 \end{matrix}]$