SOLUTION: what will be the determinant of |1 0 0 | |2 cos x sin x | |3 sin x cos x | a.1 b.0 c.cos 2x d.sin 2x

Algebra ->  Matrices-and-determiminant -> SOLUTION: what will be the determinant of |1 0 0 | |2 cos x sin x | |3 sin x cos x | a.1 b.0 c.cos 2x d.sin 2x      Log On


   

Question 1101917: what will be the determinant of
|1 0 0 |
|2 cos x sin x |
|3 sin x cos x |
a.1
b.0
c.cos 2x
d.sin 2x
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
Apply co-factoring the determinant along the first row of the matrix, and you will get


determinant = cos^2(x) - sin^2(x) = cos(2x).

About co-factoring determinant see the lesson
    - Co-factoring the determinant of a 3x3 matrix
in this site.