If $$A=aij3$$×$$3$$ and $$aij=i(i+j)$$ then trace of A.

$$A=aij3$$×$$3$$ $$aij=i(i+j)$$ (since$$ $$i=j) trace of $$A=$$ $$2(12+22+32)=28$$

Operations of matrix

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Question

If $A = {[a_{ij}]}_{3 \times 3}$ and $a_{ij} = i (i + j)$ then trace of A.

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Solution

$A = {[a_{ij}]}_{3 \times 3} a_{ij} = i (i + j) (\sin c e i = j) t r a c e o f A = 2 (1^{2} + 2^{2} + 3^{2}) = 28$

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