082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

320 Chapter 8 Matrix algebra
where
⎛ ⎞ ⎛ ⎞ ⎛ ⎞
3 2−1 4 x
A = ⎝2−1 2⎠ B = ⎝10⎠ X = ⎝y⎠
1−3−4 5 z
Inordertosolvetheseequationsinatechnicalcomputinglanguagethematricesneedto
be loaded into memory. InMATLAB ® wewould type
A = [3,2,−1;2,−1,2;1,−3,−4]
B = [4;10;5]
We note that commas are used to separate entries on the same row and semicolons are
used toseparate different rows.
ThevalueofX canbeobtainedbythemethodofmatrixinversion.Thecodeforthisis
X =inv(A) ∗B
Alternatively,X can be obtained by Gaussian elimination. The code for thisis
X=A\B
Gaussian elimination is the usual method of solving systems of linear equations in
MATLAB ® because it is computationally efficient. If we run this three-line program
using MATLAB ® then weobtain
A = [3,2,−1;2,−1,2;1,−3,−4]
B = [4;10;5]
X=A\B
X = 3.0000
−2.0000
1.0000
and sox = 3.0000, y = −2.0000, z = 1.0000.
We see that MATLAB ® is a powerful tool for carrying out matrix calculations. Part
ofitspowerderivesfromtheextremelyhigh-levelnatureofitscommands.Acommand
suchasinv(A)wouldrequiretypically50linesifwritteninanormalhigh-levellanguage
such as Cor FORTRAN.
Engineeringapplication8.6
SolutionofanelectricalnetworkusingMATLAB®
Consider again the electrical network of Engineering application 8.3. Write the
MATLAB ® code tosolve thisnetwork.
Solution
TheequationsareoftheformV =RI ′ whereV isthevoltagevectorofthenetwork,
RisthematrixofresistorvaluesandI ′ isthecurrentvectorofthenetwork.Weknow
V andRand we wish to obtainI ′ . Using the values of Engineering application 8.3
wecan write
➔