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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

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

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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