mathodman Posted March 17, 2020 Share Posted March 17, 2020 https://mathforums.com/threads/calculate-a-determinant-of-specific-a-matrix.348091/ Link to comment Share on other sites More sharing options...
mathematic Posted March 17, 2020 Share Posted March 17, 2020 There is a standard procedure to calculate the determinant of a 3x3 matrix. Link to comment Share on other sites More sharing options...
taeto Posted March 18, 2020 Share Posted March 18, 2020 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. Link to comment Share on other sites More sharing options...
mathodman Posted March 18, 2020 Author Share Posted March 18, 2020 14 hours ago, mathematic said: There is a standard procedure to calculate the determinant of a 3x3 matrix. its not, look at descriptions above Link to comment Share on other sites More sharing options...
taeto Posted March 18, 2020 Share Posted March 18, 2020 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? Link to comment Share on other sites More sharing options...
uncool Posted March 18, 2020 Share Posted March 18, 2020 The point of the problem is to use induction and the properties of determinants to find the answer, not to find each determinant separately. Link to comment Share on other sites More sharing options...
taeto Posted March 18, 2020 Share Posted March 18, 2020 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. Link to comment Share on other sites More sharing options...
mathodman Posted April 17, 2020 Author Share Posted April 17, 2020 (edited) 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, 2020 by mathodman Link to comment Share on other sites More sharing options...
taeto Posted April 18, 2020 Share Posted April 18, 2020 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. Link to comment Share on other sites More sharing options...
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