How do you find the determinant

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SUMMARY

The discussion centers on finding the value of 'a' in a system of equations that results in no solution. The primary method suggested is calculating the determinant of the matrix formed by the coefficients of the equations and equating it to zero. This indicates that the matrix is singular, leading to either no solution or infinitely many solutions, particularly when 'a' equals 1, making the row vectors linearly dependent. The conversation emphasizes the importance of understanding the implications of determinant values in linear algebra.

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http://users.on.net/~rohanlal/11Untitled.jpg
How do I find the value of a for which there will be no solution?
Do you find the determinant, equate it to 0 and solve for a?
 
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One perfectly good method would be to try to solve that system of equations by the usual "elimination" methods (I would be inclined to subtract one equation from the other) and see what values of a make it impossible to solve the equationl (For example, you can't divide by 0.)

By the way, the question (which I notice is NOT part of the copied statement) is not well phrased. The is NO value of a "for which there will be no solution". There is a value of a for which either there is no solution or there are an infinite number of solutions, depending on b.
 
by making a 1 you are making the matrix cingular because the row vectors are now linearlly dependent. I think the method you're using should work also... You would get
a-1 = 0...
 
Ry122 said:
http://users.on.net/~rohanlal/11Untitled.jpg
How do I find the value of a for which there will be no solution?
Do you find the determinant, equate it to 0 and solve for a?

Two straight lines will always intersect except if what about the lines are the same?
 
Last edited by a moderator:

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