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

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

10 hours ago, mathematic said:

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

His matrices are not given explicitly though.

14 hours ago, mathematic said:

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

its not, look at descriptions above

The inverse of the matrix on the right is a known "constant" matrix, depending on the six parameters. Is it known what it is? You appear to assume that it is invertible, how you do know it?   

The point of the problem is to use induction and the properties of determinants to find the answer, not to find each determinant separately.

Induction, absolutely. But even that will not work unless the statement is true. And in a case like \(a_0=a_1=a_2=k=l=m=0\) 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. 

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

Edited April 17, 20205 yr by mathodman

If there exists a solution for sure, then there has to be an assumption which says, or implies, that the matrix on the right hand side of the equation is invertible. Something is missing from your original explanation which allows us to make such a determination.