ndsolve interpolatingfunctions not shown/evaluated

Question

Using this technique from Simon, I want to solve a matrix differential equation with a matrix that contains an explicit time-dependence(our variable), but I want to be able to solve this problem for a generic number of functions K+1 thus auto-indexing them. My code, stripped of a few things which don't seem to be the problem, (with I= imaginary unit):

K=2;

dl = ConstantArray[ 1/2 Exp[-I t], K];       %defining M
dm = Array[(# - 1)^2 &, K + 1];
dr = ConstantArray[1/2 Exp[I t], K];
M = SparseArray[{Band[{1, 2}] -> dr, Band[{1, 1}] -> dm, 
Band[{2, 1}] -> dl}] // Normal

a[t_] := Table[g[k][t], {k, 0, K}]          %defining a as a list of functions g

NDSolve[{a'[t] == I *M.a[t], g[0][0] == 0, g[1][0] == 1, g[2][0] == 0}, {g[0], g[1], g[2]}, {t, 0, 10}][[1, All, 2]] //Abs
%solving the diff. eq.

Which returns a list of three InterpolatingFunctions with output scalar as I would expect. However,

Plot[%,{t,0,10}]

Only draws axes without any graphs. But I solved these equations for K=2 beforehands in another way(but still with DSolve) and saw some results which should also be shown the domain of this graph, but are missing. Similarly, function evaluation for a random value of t

%%[1]

Doesn't give a number either.

My intention when this works for a generic K is add a manipulate to change some parameters I put equal to one now and make the whole thing a function of K.

Answer 1

sol = NDSolveValue[{a'[t] == I*M.a[t], g[0][0] == 0, g[1][0] == 1, 
                    g[2][0] == 0}, {g[0], g[1], g[2]}, {t, 0, 10}];

Plot[Abs /@ Through[sol[t]], {t, 0, 10}, Evaluated -> True]