mathodman

On 3/18/2020 at 8:56 PM, taeto said:

Induction, absolutely. But even that will not work unless the statement is true. And in a case like a0=a1=a2=k=l=m=0 the inverse of the determinant on the right does not exist. I am asking about the condition to ensure that the equation in the OP makes sense at all. 

Hi, yeah it definitely makes sense, this is a problem from an old exam so there must be a solution for sure

14 hours ago, mathematic said:

There is a standard procedure to calculate the determinant of a 3x3 matrix.

its not, look at descriptions above

https://mathforums.com/threads/calculate-a-determinant-of-specific-a-matrix.348091/

I don't know, i kind of got stuck on this one. 

22 hours ago, hypervalent_iodine said:

!

Moderator Note

We do not do other people's homework for them. Please show some attempt at an answer and explain here you are stuck. 

 

Its not a homework, lol. Just an interesting problem, that i don't quite understand. I think that the only option is that A matrix is zero matrix or maybe i have forgotten some theorem  or criteria

Let for j = 0,. . ., n aj = a0 + jd, where a0 and d are fixed real numbers.
Calculate the determinant of the matrix A of size (n + 1) × (n + 1). Matrix A is below

Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.