Understanding the Matrix of Minors

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The matrix of minors refers to a matrix where each element is the minor of the corresponding element in the original matrix. It is distinct from the adjoint matrix, which involves taking the cofactors—minors adjusted for sign—and then transposing that matrix. To calculate the matrix of minors, one must first identify the minors for each element in the given matrix. The discussion clarifies that while both concepts are related, they serve different purposes in matrix operations. Understanding this distinction is crucial for solving equations like Ax=b correctly.
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can anyone explain to me what the matrix of minors is?
 
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Is it possible you mean the minors of a matrix?
 
no, I've been given the question:

Ax=b.A=(301), x= transverse of {x,y,z} and b=transverse of {5,2,-1}
(132)
(120)

and the first thing it asks me to do is calculate the matrix of minors. is this just another term for the adjoint matrix or something?
 
Well the "matrix of minors" (of a square matrix) would be the matrix where each element is the minor of the number which was in that position, which isn't the same as the adjoint yet.
For the adjoint, you'd have to take the cofactors (which is the minors + sign taken into account) and transpose that. So adjoint = transpose of cofactor matrix.
 

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