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A simple model for estimating the temperature distribution on a square plate gives rise to a linear system of equations. To construct the appropriate linear system, we use the following information: The square plate is perfectly insulated on its top and bottom so that the only heat flow is through the plate itself. The four edges are held at various temperatures. To estimate the temperature at an interior point on the plate, we use the rule that it is the average of the temperatures at its four compass-point neighbors, to the west, north, east and south Estimate the temperatures Find the temperatures T1, T2, T3, T4 of the four evenly spaced interior points of the plate shown in the figure below, using the triangular matrix method. (When solving, equations that give average temperature should be written as homogeneous linear equations.) 100 T2 21 08 T3 0°

A simple model for estimating the temperature distribution on a square plate gives rise to a linear system of equations. To construct the appropriate linear system, we use the following information: The square plate is perfectly insulated on its top and bottom so that the only heat flow is through the plate itself. The four edges are held at various temperatures. To estimate the temperature at an interior point on the plate, we use the rule that it is the average of the temperatures at its four compass-point neighbors, to the west, north, east and south Estimate the temperatures Find the temperatures T1, T2, T3, T4 of the four evenly spaced interior points of the plate shown in the figure below, using the triangular matrix method. (When solving, equations that give average temperature should be written as homogeneous linear equations.) 100 T2 21 08 T3 0°

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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A simple model for estimating the temperature distribution on a square plate gives rise to a linear system of equations. To construct the appropriate linear system, we use the following information: The square plate is perfectly insulated on its top and bottom so that the only heat flow is through the plate itself. The four edges are held at various temperatures. To estimate the temperature at an interior point on the plate, we use the rule that it is the average of the temperatures at its four compass-point neighbors, to the west , north, east and south Estimate the temperatures Find the temperatures T1, T2, T3, T4 of the four evenly spaced interior points of the plate shown in the figure below, using the triangular matrix method. (When solving, equations that give average temperature should be written as homogeneous linear equations.) 100 T T2 80 21 T3 T 0°
Transcribed Image Text:A simple model for estimating the temperature distribution on a square plate gives rise to a linear system of equations. To construct the appropriate linear system, we use the following information: The square plate is perfectly insulated on its top and bottom so that the only heat flow is through the plate itself. The four edges are held at various temperatures. To estimate the temperature at an interior point on the plate, we use the rule that it is the average of the temperatures at its four compass-point neighbors, to the west , north, east and south Estimate the temperatures Find the temperatures T1, T2, T3, T4 of the four evenly spaced interior points of the plate shown in the figure below, using the triangular matrix method. (When solving, equations that give average temperature should be written as homogeneous linear equations.) 100 T T2 80 21 T3 T 0°
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