Page 780 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Systems of linear equations with complex coefficients arise in various applications. Without going into detail, we note that
all the results about linear systems studied in Chapters 1 and 2 carry over without change to systems with complex
coefficients. Note, however, that a few results studied in other chapters will change for complex matrices.

EXAMPLE 4 A Linear System with Complex Coefficients
Use Cramer's rule to solve

Solution

Thus the solution is , .

We conclude this section by listing some properties of the complex conjugate that will be useful in later sections.

THEOREM 10.2.3

Properties of the Conjugate
For any complex numbers z, , and :

(a)

(b)
(c)
(d)