4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, €3} B₂ = {1, t, t²} V₂ =R[t]

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4 Consider The Following Three Vector Spaces With Corresponding Basis V R B E E2 3 B 1 T T V R T 1 (103.13 KiB) Viewed 56 times

4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, €3} B₂ = {1, t, t²} V₂ =R[t]<2 V3 = M2x2 (R) B3 (a) (1 point) Compute [7]B - 6)6)( 96 ) Now consider the following two linear transformations: T() - Tb)=a+b-ct + at² S(ao + a₁t+ a₂t²) = ao-a₂ a1 ao+a₁ a₂ (b) (1 point) Compute [S]B (c) (2 points) Compute [So T]B, and verify that [ST]B₁ = [S]₂[T]²₁