determinant fast method

[lean minnow]

I have solved it by cubic equation but it takes time is there any short method?

[chilly light]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[covert ore]

Well there is a fast method to solve this take the same matrice as presented but with only 0 instead of x and with opposite coefficients ( let’s call it A)

Here the matrice presented is x*I3 -A

And for x in C the determinant of x*I3-A is 0 if and only if x is an eigenvalue of A

here 5 is actually an eigenvalue

Because if you replace x by 5 the matricés rank is 2 thus it’s determinant is 0

Then knowing that 5 is an eigenvalue and that the determinant is 0 you can directly calculate the determinant with respect to x by substracting the last column to the first one and then calculating the determinant by developing using cofactors

Then factor by (x-5)

You’ll have a quadratic to solve

[lean minnow]

I didn't understand the starting line

[covert ore]

Forget it I just realized it’s not really important

But look at the matrice for x=5

[lean minnow]

Yes i take x=5

First and third colomn look same so determinant 0

[covert ore]

Yep

So now you can factor your cubic