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Question

Construct a 2 × 3 matrix whose elements aij are given by :
(i) aij = i . j
(ii) aij = 2i − j
(iii) aij = i + j
(iv) aij = (i+j)22

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Solution

i

Here,
aij=i . j, 1i2 and 1j3

a11=1×1=1, a12=1×2=2, a13=1×3=3a21=2×1=2, a22=2×2=4 and a23=2×3=6

Required matrix = A = 123246

ii

Here,
aij=2i-j

a11=21-1=2-1=1 , a12=21-2=2-2=0 , a13=21-3=2-3=-1a21=22-1=4-1=3 , a22=22-2=4-2=2 and a23=22-3=4-3=1

Required matrix = A = 10-1321

iii
Here,
aij=i+j

a11=1+1=2 , a12=1+2=3 , a13=1+3=4a21=2+1=3 , a22=2+2=4 and a23=2+3=5

Required matrix = A = 234345

iv

Here,
aij=i+j22

a11=1+122=222=42=2 , a12=1+222=322=92 , a13=1+322=422=162=8a21=2+122=322=92 , a22=2+222=422=162=8 and a23=2+322=522=252

Required matrix = A = 2928928252

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