Calculating an n X n determinant

[TGV320]

Homework Statement

Help in order to solve a determinant

Relevant Equations

Determinants

Hello,

I need some advice because I just can't figure out how to solve the problem. I could try to make the determinant triangular by adding all the b together, but that doen't seem a good way of solving the problem. Is there any direction I should be thinking of?

Thanks

 

[PeroK]

Why not calculate the determinant for ##n = 2, 3, 4## and see whether a pattern emerges?

 

[topsquark]

Homework Statement: Help in order to solve a determinant
Relevant Equations: Determinants

Hello,

I need some advice because I just can't figure out how to solve the problem. I could try to make the determinant triangular by adding all the b together, but that doen't seem a good way of solving the problem. Is there any direction I should be thinking of?

View attachment 335323Thanks

Hint: Follow PeroK's advice and find the determinant by expanding along the bottom row.

-Dan

 

[Hill]

By considering the Leibniz formula, one can figure out that only some terms survive, where the permutations do not contain zeroes.

 

[martinbn]

Multiply the ##i^{th}## row by ##-a_i## and add it to the first. You just need to see what the top left element will be.

 

[TGV320]

Hi,
Thanks for the advice.
I have figured it out,though I never thought about getting the answer by experimenting on it, always thought it to n. That way of doing it with n=2 then 3 is quite illuminating.