Change of basis
Basis B={<1,1>,<1,-1>}. Vector v=<4,2>. Solve a<1,1>+b<1,-1>=<4,2>.
- Equations a+b=4 and a-b=2.
- Defend the transfer, name its boundary, and leave an auditable reasoning trail.
vectors, matrices, systems, spaces, and eigenstructure
Basis B={<1,1>,<1,-1>}. Vector v=<4,2>. Solve a<1,1>+b<1,-1>=<4,2>.
Pause. Find what matters. Then make your move.