Use the decomposition result (1.2.10) to express a ij from Exercise 1.1 in terms of the sum

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Use the decomposition result (1.2.10) to express aij from Exercise 1.1 in terms of the sum of symmetric and antisymmetric matrices. Verify that a(ij) and a[ij] satisfy the conditions given in:
the last paragraph.

Equation 1.2.10

aij z (aij + aji) +z (aij  aji) = a(yj) + a[i]

Data from exercise 1.1

For the given matrix/vector pairs, compute the following quantities: aii, aijaij, aijajk, aijbj, aijbibj, bibj, bibi. For each case, point out whether the result is a scalar, vector or matrix. Note that aijbj is actually the matrix product [a]{b}, while aijajk is the product [a][a].

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