Finding values that make a determinate = 0

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In summary, the conversation discusses finding the values of a that make the determinant of a given matrix equal to 0. The individual presents their attempt at a solution using the Cofactor theorem but runs into difficulty finding the correct roots. Another person suggests double checking the calculation and trusting the math instead of intuition. The individual then realizes their error and thanks the other person for their help.
  • #1
DanielJackins
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Homework Statement



Given the matrix A = {a, 3, 8}{a, -3, 4}{7, -4, a} find all values of a that make det(A) = 0.

(each {} is a row in the matrix, 3x3)

The Attempt at a Solution



I've expanded it out using the Cofactor theorem, ie. a11c11 + a21c21 + a31c31, and I come out with a polynomial, -2(3a^2+8a-126) which I equate to 0. Solving for the quadratic gives ugly roots which I can't see being correct.

Thanks for any help
 
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  • #2
Doing a very quick calculation, are you sure your '-126' shouldn't be '126'? (When you factor out the -2, shouldn't you have a positive 126 left?)
 
  • #3
Well according to maple your determinant is correct. You should really trust the math instead of your intuition about what you can see being correct.
 
  • #4
Huh, it was correct :P I just figured the answer would be integers. Thanks for the help :)
 

1. How do you find values that make a determinate equal to zero?

To find the values that make a determinate equal to zero, you can use the quadratic formula or factor the equation. The values that satisfy the equation and make the determinate equal to zero are called the roots of the equation.

2. Why is it important to find values that make a determinate equal to zero?

Finding the values that make a determinate equal to zero is important because it helps us solve equations and find the points where the function intersects the x-axis. This is useful in many fields of science and mathematics.

3. Can there be more than one set of values that make a determinate equal to zero?

Yes, there can be more than one set of values that make a determinate equal to zero. This is because some equations have multiple roots or solutions that satisfy the equation and make the determinate equal to zero.

4. What does it mean when a determinate is equal to zero?

When a determinate is equal to zero, it means that the equation has at least one real solution. This means that there is at least one value of the variable that satisfies the equation and makes the determinate equal to zero.

5. Are there any other methods for finding values that make a determinate equal to zero?

Yes, there are other methods for finding values that make a determinate equal to zero, such as using graphical methods or numerical methods like Newton's method. These methods can be useful when the equation is not easily solvable using the quadratic formula or factoring.

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