Page 130 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

2 3 5 2 3
detA = 1 0 1 1 0
2 1 0 2 1
or
)
)
1
detA= ( 2 × 0 × 0 + ( 3 × × 1 + ( 5 × 1 × 1 )
)
)
)
– ( 2 × 0 × 5 – ( 1 × 1 × 2 – ( 0 × 1 × 3 = 11 – 2 = 9
Likewise,
–
23 4 23
–
–
detB = 10 2 1 – 2
–
–
–
05 6 2 – 6
or
)
)
)
]
detB= [ 2 × × – ( 6 ] ) + – ( [ 3 × – ( 2 × 0 + – ( [ 4 × 1 × – ( 5 ] )
0
)
)
]
)
1
– [ 0 × 0 × – ( 4 ] ) – – ( [ 5 × – ( 2 × 2 – – ( [ 6 × × – ( 3 ] ) = 20 – 38 = – 18
Check with MATLAB:
A=[2 3 5; 1 0 1; 2 1 0]; det(A) % Define matrix A and compute detA
ans =
9
B=[2 −3 −4; 1 0 −2; 0 −5 −6]; det(B) % Define matrix B and compute detB
ans =
-18
The MATLAB user−defined function file below can be used to compute the determinant of a
3 × 3 matrix.
% This file computes the determinant of a 3x3 matrix
% It must be saved as function (user defined) file
% det3x3.m in the current Work Directory. Make sure
% that his directory is added to MATLAB's search
% path accessed from the Editor Window as File>Set Path>
% Add Folder. It is highly recommended that this
% function file is created in MATLAB's Editor Window.
%
function y=det3x3(A);
y=A(1,1)*A(2,2)*A(3,3)+A(1,2)*A(2,3)*A(3,1)+A(1,3)*A(2,1)*A(3,2)...
−A(3,1)*A(2,2)*A(1,3)−A(3,2)*A(2,3)*A(1,1)−A(3,3)*A(2,1)*A(1,2);
%
% To run this program, define the 3x3 matrix in
% MATLAB's Command Window as A=[....] and then
% type det3x3(A) at the command prompt.

4−12 Numerical Analysis Using MATLAB® and Excel®, Third Edition

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