uz < and u4 at the points P1, P2, P3, and P4, respectively, are given by u2 + u4 + 100+100 4 200 + u3 + u1 + 100 u2 4 200 + 100 + u4 + u2 uz 4 u3 + 100 + 100+u1 4 (a) Show that this system of equations can be written as the matrix equation -4 1 1 (–200) 1 -4 1 u2 -300 1 -4 1 uz -300 1 1 -4, -200, (b) Solve the system in (a) by finding the inverse of the coefficient matrix. u = 200 P2 P3 u = 100 u = 100 P1 P4 4 = 100
uz < and u4 at the points P1, P2, P3, and P4, respectively, are given by u2 + u4 + 100+100 4 200 + u3 + u1 + 100 u2 4 200 + 100 + u4 + u2 uz 4 u3 + 100 + 100+u1 4 (a) Show that this system of equations can be written as the matrix equation -4 1 1 (–200) 1 -4 1 u2 -300 1 -4 1 uz -300 1 1 -4, -200, (b) Solve the system in (a) by finding the inverse of the coefficient matrix. u = 200 P2 P3 u = 100 u = 100 P1 P4 4 = 100
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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Question

Transcribed Image Text:uz < and u4 at the points P1, P2, P3, and P4, respectively, are given by
u2 + u4 + 100 + 100
U1 =
4
200 + u3 + u1 + 100
U2
4
200 + 100 + U4 + u2
U3
4
u3 + 100 + 100 + u1
U4 =
4
(a) Show that this system of equations can be written as the matrix equation
-4
1
1
– 200\
u1
1
-4
1
U2
-300
1
-4
1
Uz
-300
1
1
-4
-200
(b) Solve the system in (a) by finding the inverse of the coefficient matrix.
u = 200
P2
P3
u = 100
u = 100
P4
4 = 100

Transcribed Image Text:4. Consider the square plate shown in the figure, with the temperatures as indicated on each
side. Under some circumstances it can be shown that the approximate temperatures u1, u2,
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