The array below represents the temperatures (in degrees Fahrenheit) of certain points on theinterior and boundary of a metal plate: 30 30
15 T1 T2 45
15 T3 T4 45
60 60

Assume that the temperature at each point is theaverageof the temperatures at the four neighboring points(left, right, above, and below).Set up (do not solve)a system of four linear equations whose solution gives the four temperature T1,T2,T3, andT4. (Your linear equations should all be written instandard form, meaning a linear combination ofthe variables set equal to a constant.)

Step-by-step explanation:

Given

Required

Set up 4 linear equations to solve for T1,T2,T3, andT4

From the question, we understand that each temperature is the average of the 4 surrounding temperatures.

So, we have:

For T1, the surrounding temperatures are: 30, 15, T3 and T2.

The average is:

Multiply through by 4

Equate variables to constant

For T2, the surrounding temperatures are: T1, T4, 45 and 30.

The average is:

Multiply through by 4

Equate variables to constant

For T3, the surrounding temperatures are: 60, 15, T1 and T4

The average is:

Multiply through by 4

Equate variables to constant

For T4, the surrounding temperatures are: 60, 45, T2 and T3

The average is:

Multiply through by 4

Equate variables to constant

So, the equations are:

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step-by-step explanation:

step-by-step explanation:

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