If A=aimxn and aij=i(i+j) then trace of A= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$\frac{n (n + 1) (2 n + 1)}{6}$
B
$\frac{n (n + 1) (2 n + 1)}{3}$
C
$\frac{n (n + 1)}{2}$
D
$\frac{n^{2} (n + 1)^{2}}{4}$

Solution:

$Given A = [a_{i j}] and a_{i j} = i (i + j) a_{n, n} = n (n + n) = 2 n^{2} Trace of A = a_{1, 1} + a_{2, 2} + a_{3, 3} + \dots \dots \dots . . . + a_{n, n} A = 2 [1 + 4 + 9 + . . . . . . . . n^{2}] \begin{array}{l} A = 2 \times [\frac{n (n + 1) (2 n + 1)}{6}] \\ A = \frac{n (n + 1) (2 n + 1)}{3} \end{array}$

$If A = {[a_{i}]}_{m x n} and a_{i j} = i (i + j) then trace of A =$

Solution:

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