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I attempted to solve it in the following way:

v1 = 2sin(2t+45) // given

= 2[sin(2t)cos(45) + cos(2t)sin(45)]

= √2[sin(2t) + cos(2t)]

I use a matrix for the loops:

A =

[2 -1 -1

-1 3 -1

-1 -1 3]

b =

[√2

0

0]

I'm wondering what format the final solution should be in. Should it be Isin(2t+45) or I[sin(2t) + cos(2t)]?

Btw, I got √2/2 for the magnitude of both the currents.

Any input is appreciated. Thanks in advance.