Page 129 - Numerical Analysis Using MATLAB and Excel

Determinants

y=A(1,1)*A(2,2)−A(1,2)*A(2,1);
%
% To run this program, define the 2x2 matrix in
% MATLAB's Command Window as A=[....] and then
% type det2x2(A) at the command prompt.

Let be a matrix of order 3, that is,
A

a 11 a 12 a 13
A = a 21 a 22 a 23 (4.15)

a 31 a 32 a 33

then, detA is found from

a
detA = a 11 22 33 + a 12 23 a 31 + a 11 22 33
a
a
a
a
a
a – 11 22 a 33 – a 11 22 a 33 – a 11 22 a 33 (4.16)
a
a
A convenient method to evaluate the determinant of order 3, is to write the first two columns to
the right of the 3 × 3 matrix, and add the products formed by the diagonals from upper left to
lower right; then subtract the products formed by the diagonals from lower left to upper right as
shown on the diagram of the next page. When this is done properly, we obtain (4.16) above.
a 11 a 12 a 13 a 11 a 12 −

a 21 a 22 a 23 a 21 a 22
a 31 a 32 a 33 a 31 a 32 +

This method works only with second and third order determinants. To evaluate higher order
determinants, we must first compute the cofactors; these will be defined shortly.

Example 4.5
Compute detA and detB given that

2 3 5 2 – 3 – 4
A = 1 0 1 and B = 1 0 – 2
2 1 0 0 – 5 – 6
Solution:

Numerical Analysis Using MATLAB® and Excel®, Third Edition 4−11
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