Consider the following system of equation: $$ x_1' = (2-t)x_1+(t-1)x_2 \\ x_2' = 2(1-t)x_1+(2t-1)x_2.\\ $$
We, therefore, have a system of the following form $$\dot{X}=A(t)X(t).$$ I am not sure how to go about solving this system since $A$ is not a matrix of constants. Any hints will be much appreciated.