ME
–
210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
Cramer’s Rule
A useful application of determinants to the solution of linear algebraic equations
[A] [x] = [b]
is the
Cramer’s rule
, which can be used only when the coefficient matrix [A] is a
non-singular and square
matrix.
Note that when [A] is a nonsingular matrix, it has a nonzero determinant
(that is, det[A] ≠ 0, hence its rank is
full
(that is rank[A] = n), hence rank[A] = rank[A¦b],
thereby the solution
exists
and is
unique
.

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