Throughout this homework, please note that the symbol $lon$ only presents the third order Permutation Calculate the following expression, finally to convert your result into the direct notation

$(4{10}^{\text{'}})$

For $i,j,k,m,n,l=1,2,3,,$ are constant scalars. For example,

$lo{n}_{\text{i}\text{j}\text{k}}lo{n}_{\text{i}\text{j}\text{k}}={}_{ii}{}_{jj}-{}_{ij}{}_{ji}=(TrI{)}^2-Tr{I}^2=6$

$lo{n}_{\text{j}\text{i}\text{k}}lo{n}_{mnk}{A}_{im}{B}_{jn}$

${}_{mm}{}_{}$

$A_{ij}{}_{ik}+A_{jk}$

${}_{ij}{}_{kl}{E}_{kl}$

tensor on $R^3,$ and $$ only presents the Kronecker delta on $R^n.$

Fill out the following table for each of the tensors $(4{10}^{\text{'}})$

The indices $i,j=1,2,3,$ while $m,n,p,q=1,2.$