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SetDelayed problems with matrix operation


Given a square matrix such as

A={{-3, 0, 0.05}, {0.8, -0.01, 0}, {0, 0.01, -0.05}}

I wish evalute the expresion:

{ x1[t_], x2[t_], x3[t_]} : = MatrixExp[A t].{b1, 0, 0}

I receive the message

SetDelayed::"shape": "Lists{ x1[t_], x2[t_], x3[t_] } and  MatrixExp[A t)] .
{b1, 0, 0} are not the same shape."

But it is known that when MatrixExp[A t].{b1, 0, 0} will be evaluate , given
a  value for t,  the solution  will be already a list of the same shape that
Lists{ x1[t_], x2[t_], x3[t_]} 

For instance: 

MatrixExp[A t].{b1, 0, 0}/.t->3 it work fine.

How it will be build the the expresion { x1[t_], x2[t_], x3[t_]} : =
MatrixExp[A t].{b1, 0, 0} to be evaluated?





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