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Paticular integral for vector differential equation

PI for DE.png

Hi guys,

Question is above. I am stuck on part (c). The complementary function has a term of the form Axe^(2t), hence for part (c), the particular integral will be y = cte^(2t), where c is a column vector (c_1, c_2, c_3).

But when I try to solve for c I get something hideous and most likely I am doing it wrong since it can't be that messy. How would you do this given we are dealing with vectors?

Any help is appreciated.

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