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Use a software program or a graphing utility with matrix capabilities and Cramer's Rule to solve -8x1 + 7x2 10x3 = -158 12x1 + 3x2 5x3 = 15x1 - 9x2 + 2x3 = 3 129

Use a software program or a graphing utility with matrix capabilities and Cramer's Rule to solve -8x1 + 7x2 10x3 = -158 12x1 + 3x2 5x3 = 15x1 - 9x2 + 2x3 = 3 129

Calculus: Early Transcendentals
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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**Solving Systems of Equations Using Matrix Capabilities and Cramer's Rule** To solve the given system of linear equations, we can use a software program or graphing utility with matrix capabilities. The equations to solve are as follows: 1. \(-8x_1 + 7x_2 - 10x_3 = -158\) 2. \(12x_1 + 3x_2 - 5x_3 = 3\) 3. \(15x_1 - 9x_2 + 2x_3 = 129\) These equations form a system that can be represented in matrix form as \(Ax = b\), where: \[A = \begin{bmatrix} -8 & 7 & -10 \\ 12 & 3 & -5 \\ 15 & -9 & 2 \end{bmatrix}\] \[x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\] \[b = \begin{bmatrix} -158 \\ 3 \\ 129 \end{bmatrix}\] Using Cramer's Rule or a matrix-solving tool, we aim to find the values of \(x_1\), \(x_2\), and \(x_3\). **Note:** If the system has no solution or if the determinant of matrix \(A\) is zero, indicating that the inverse of \(A\) does not exist, it will not be possible to solve the system using these methods and it will be deemed "impossible". Given the result shown in the image indicating "IMPOSSIBLE", it suggests that the system does not have a valid solution possibly due to dependence among the equations or an inconsistency. For students, understanding when and why a system of equations is unsolvable is as crucial as learning to solve those that have solutions. For practical applications, always verify the determinant and consistency of the system before applying solving techniques.
Transcribed Image Text:**Solving Systems of Equations Using Matrix Capabilities and Cramer's Rule** To solve the given system of linear equations, we can use a software program or graphing utility with matrix capabilities. The equations to solve are as follows: 1. \(-8x_1 + 7x_2 - 10x_3 = -158\) 2. \(12x_1 + 3x_2 - 5x_3 = 3\) 3. \(15x_1 - 9x_2 + 2x_3 = 129\) These equations form a system that can be represented in matrix form as \(Ax = b\), where: \[A = \begin{bmatrix} -8 & 7 & -10 \\ 12 & 3 & -5 \\ 15 & -9 & 2 \end{bmatrix}\] \[x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\] \[b = \begin{bmatrix} -158 \\ 3 \\ 129 \end{bmatrix}\] Using Cramer's Rule or a matrix-solving tool, we aim to find the values of \(x_1\), \(x_2\), and \(x_3\). **Note:** If the system has no solution or if the determinant of matrix \(A\) is zero, indicating that the inverse of \(A\) does not exist, it will not be possible to solve the system using these methods and it will be deemed "impossible". Given the result shown in the image indicating "IMPOSSIBLE", it suggests that the system does not have a valid solution possibly due to dependence among the equations or an inconsistency. For students, understanding when and why a system of equations is unsolvable is as crucial as learning to solve those that have solutions. For practical applications, always verify the determinant and consistency of the system before applying solving techniques.
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