CALCULUS Understanding
Its Concepts and Methods
CALCULUS Understanding
Its Concepts and Methods
Determinant
The determinant of a
2 × 2
matrix
is defined by the formula
ad -
bc.
It is denoted by vertical brackets,
so
The determinant of a
3 × 3
matrix
is defined by the formula
,
or
The
determinant of an
n ×
n
matrix
A = [aij]
is defined inductively by the formula
where
Aij
is the
i,j-cofactor---the
determinant of the matrix obtained by removing the
ith
row and the
jth
column, multiplied by
(-1)i+j.
Any row
(1 ≤ i ≤ n)
can be used in the computation.
.
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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.