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Use an inverse matrix to solve each system of linear equations. (a) x+ 2y - 1 x- 2y - -3 (X, y) = (b) x+ 2y = 11 X- 2y - -5 x, y)%3D

Use an inverse matrix to solve each system of linear equations. (a) x+ 2y - 1 x- 2y - -3 (X, y) = (b) x+ 2y = 11 X- 2y - -5 x, y)%3D

Advanced Engineering Mathematics
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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**Solving Systems of Linear Equations Using Inverse Matrix** Given below are two systems of linear equations. Use an inverse matrix to find the solution for each system. **(a)** 1. \( x + 2y = 1 \) 2. \( x - 2y = -3 \) Find \((x, y)\): \[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \] **(b)** 1. \( x + 2y = 11 \) 2. \( x - 2y = -5 \) Find \((x, y)\): \[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \] --- In both cases, express the system of equations in matrix form and use the inverse of the coefficient matrix to solve for the variables \(x\) and \(y\).
Transcribed Image Text:**Solving Systems of Linear Equations Using Inverse Matrix** Given below are two systems of linear equations. Use an inverse matrix to find the solution for each system. **(a)** 1. \( x + 2y = 1 \) 2. \( x - 2y = -3 \) Find \((x, y)\): \[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \] **(b)** 1. \( x + 2y = 11 \) 2. \( x - 2y = -5 \) Find \((x, y)\): \[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \] --- In both cases, express the system of equations in matrix form and use the inverse of the coefficient matrix to solve for the variables \(x\) and \(y\).
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