The coordinates of the left element under this set of bases should be transposed, multiplied by the measurement matrix, multiplied by the right matrix, and then multiplied by the matrix under this set of bases.

Specific solutions:

' a 1+a2+a3=(a 1，a2，a3)( 1， 1， 1)'

' a 1=(a 1，a2，a3)( 1，0，0)'

(a 1+a2+a3，a 1)=[ 1 1]*[ 1- 1 1； - 1 2 0; 1 0 4]*[ 1 0 0]'= 1