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An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. Assume the plate shown in the figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let $T_{1}, \ldots, T_{4}$ denote the temperatures at the four interior nodes of the mesh in the figure. The temperature at a node is approximately equal to the average of the four nearest nodes - to the left, above, to the right, and below.' For instance,$$T_{1}=\left(10+20+T_{2}+T_{4}\right) / 4, \quad \text { or } \quad 4 T_{1}-T_{2}-T_{4}=30$$(PICTURE NOT COPY)Write a system of four equations whose solution gives estimates for the temperatures $T_{1}, \ldots, T_{4}$

$4 T_{1}-T_{2}-T_{4}=30$$4 T_{2}-T_{1}-T_{3}=60$$4 T_{3}-T_{2}-T_{4}=70$$4 T_{4}-T_{1}-T_{3}=40$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 1

Systems of Linear Equations

Introduction to Matrices

Laiba K.

September 29, 2020

The following diagram shows part of the central section of UC Davis campus. Assume that the streets are one way, and f1,…,f4 represent the average numbers of vehicles per minute entering and leaving intersections A, B, C, and D during business hours. (a)

For what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infinitely many solutions?

For what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infinitely many solutions? x+y+ kz=1

Marc S.

March 14, 2021

It's videos like this one that make me wonder what I'm paying for here. Simply writing the answer and saying that's the answer doesn't help.

Dk B.

December 9, 2021

Samantha L. is way too off.

Campbell University

McMaster University

Harvey Mudd College

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So for this problem, we're asked to determine the system of equations that would determine the temperatures at points 123 and four and relate the mall together. So we know that the temperature at each point is the average and sort of following. The example we have t one plus two to plus T four equals 30 before templates 23rd. Then to do the upper right corner, we'll have four times 22 plus t one plus t three equal 60. The next one would be four times t three plus two u two plus t four, and that would be 70. And finally, in the lower left corner, we would have four times t four plus t one plus t three is 40 and so we can see that each of these corresponds two its respective point and each of the right hand side here corresponds to the constants in the left hand side corresponds to all of the neighboring points

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In mathematics, the absolute value or modulus |x| of a real number x is its …

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