# solve system of linear equation $AX=b$ and define determinate for this matrix

Assume that matrix $A$ define in this form $$A=[a_{ijk}] , a_{ijk} \in F$$ ($F$ is arbitrary field ).

The size of $A$ is $m \times n \times k$ ($m$ is number of row and $n$ is number of column and $k$ is number of vector that is perpendicular on row vector and column vector ) . May I ask you to hint me about the following:

a)How can I define determinate ?

b) how can I solve system of linear equation $(AX=b )$?

Or let this matrix is $A=[a_{(i_1,i_2,..,i_n )}]$ (all entry is from $Ν×Ν×…×Ν$ to $F$ s.t $$(i_1,i_2,..,i_n)→ a_{(i_1,i_2,..,i_n )}$$ and define size of matrix like above, can we compute $a$ and $b$ for this matrix?

Thanks so much!

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A simular question was asked here: math.stackexchange.com/questions/63074/… – Tpofofn Dec 30 '12 at 12:51
@Maisam, What is your meaning by "compute a and b for this matrix"? what are "a" and "b", and which condition you want to be satisfied? – AmirHosein SadeghiManesh Jan 6 '13 at 6:51
i mean How can I define determinat how can I solve system of linear equation (AX=b) and let A=[a_{ijk}] , a_{ijk} \in F and B=[a_{ijk}] , a_{ijk} \in F how compute this product AB. – Maisam Hedyelloo Jan 18 '13 at 9:14