[10](1) GIVEN: P2={a0+a1x+a2x2∣a0,a1,a2∈R}T:P2⟶R,T(a0+a1x+a2x2)=a2 For example: T(1−x+3x2)=3 PROVE: T is a linear transformation. [10] (2) GIVEN: x=(x1,x2,x3,x4)∈R4 SOLVE: ↓:⎩⎨⎧x1+2x2−x3+x4x1+3x2+2x4−x1−2x2+x3−x4x2+x3+x4=0=0=0=0 (Express solution set of ↓ as the span(B),B L.I. B⊂R4 )
