How do you find the determinant

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To find the value of 'a' for which a system of equations has no solution, one must calculate the determinant and set it to zero. This indicates that the matrix is singular, which occurs when the row vectors become linearly dependent. The discussion highlights that there is no single value of 'a' that guarantees no solution; rather, certain values lead to either no solution or infinitely many solutions, depending on the value of 'b'. Specifically, setting 'a' to 1 makes the matrix singular. The conversation emphasizes the importance of understanding the relationship between the equations to determine the conditions for solutions.
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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?
 
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