Question

Construct a 2 × 2 matrix whose elements a_ij are given by:

`a_(ij)=e^(2ix) sin (xj)`

Answer 1

`a_(ij)=e^(2ix) sin (xj)`

Here,

`a_11=e^(2xx1xxx)sin(x xx1)= e^(2x) sin(x),  a_12= e^(2xx1xxx) sin (x xx 2)= e^(2x) sin (2x)`

`a_21= e^(2 xx 2xx x)sin (x xx 1)= e^(4x) sin (x) , a_22 = e^(2 xx 2xx x) sin (x xx 2)= 6^(4x)sin (2x)`

So, the required matrix is `[[e^(2x)sin (x)   e^(2x)sin (2x)],[e^(4x)sin (x)   e^(4x)sin (2x)]]`