Hello all. I have a queston about determinants. The question is from an exam and solutions were not published. I would like to know if my solution is correct. Please excuse me for the imperfect formatting, I am struggling with the interface. Espeacially the superscripts were supposed to be subscripts.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

The question is to compute the determinant of a matrix of polynomals of degree n-2 or less that looks like this:

F[tex]_{1}[/tex](X[tex]_{1}[/tex]) F[tex]_{1}[/tex](X[tex]_{2}[/tex]) ... F[tex]_{1}[/tex](X[tex]_{n}[/tex])

F[tex]_{2}[/tex](X[tex]_{1}[/tex]) F[tex]_{2}[/tex](X[tex]_{2}[/tex]) ... F[tex]_{2}[/tex](X[tex]_{n}[/tex])

[tex]\cdots[/tex]

[tex]\cdots[/tex]

[tex]\cdots[/tex]

F[tex]_{n}[/tex](X[tex]_{1}[/tex]) F[tex]_{n}[/tex](X[tex]_{2}[/tex]) ... F[tex]_{n}[/tex](X[tex]_{n}[/tex])

I assumed n=3 and showed that in this case the determinant is 0.

I then assumed correctness for n and want to show that this is true for n+1 thus proving by induction.

Writing the same matrix but with n+1 rows and columns, I compute the determinant using expansion by row. I "crossed out" the n+1 row and n+1 column and so have a sum of sclars (which are polynomials) multiplying the NXN matrix that I assumed has a 0 determinant. So the sum is 0 hence conculding the proff.

Is this correct?

Thank you

Tal

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Determinant question

**Physics Forums | Science Articles, Homework Help, Discussion**