Construct a 3 × 4 matrix whose elements aij are given by aij = i + 2j

(i) a_ij = i . j

(ii) a_ij = 2i − j

(iii) a_ij = i + j

(iv) a_ij = (i+j)^2/2

Answer:- (i) a_ij = i . j

The elements of a 3×4 matrix is A= ⎣a11 a12 a13 a14

a21 a22 a23 a24

a31 a32 a33 a34⎥

Applying the specified rule: aij=i+2ja11=3, a12=5, a13=7, a14=9a21=4, a22=6, a23=8, a24=10a31=5, a32=7, a33=9, a34=11

Consequently A=⎡⎢⎣3 5 7 9

4 6 8 1

0 5 7 9 11⎥⎦ is the vital matrix.