What are the values of a that make A=0?

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To determine the values of 'a' that make the determinant of matrix A equal to zero, cofactor expansion is suggested as the method of approach. The matrix A is given as a 3x3 matrix with variable 'a' in multiple positions. Participants express confusion about how to apply cofactor expansion effectively in this scenario. The discussion emphasizes the need for clarity in the calculations involved in finding the determinant. Ultimately, the goal is to identify all values of 'a' that satisfy the condition A=0.
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Homework Statement



if
A=
a 3 5
a -7 6
5 4 a

find all values of a that make A=0. Give your answer as a comma-separated list.

Homework Equations



Looks like the cofactor expansion would be used

The Attempt at a Solution



I'm really lost in this one.
 
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~Sam~ said:
Looks like the cofactor expansion would be used
What did you get by using it?
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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