Let B = {(1, 1), (2, 3)} and B′ = {(5, 2), (1, 3)} be two bases for R2. [T]B= 2 3 4 7 (a) Find (T (v))B′ , where (v)B′ = (2, −1). (b) Verify your answer in (a).

Determine L[t² u(t – 10)]. -

d d Calculate[r₁(t) r₂(t)] and [r₁(t) × r²(t)] first by differentiating the product directly and then by applying the formulas d dr₂ dr₁ [r₁(t) · r₂(t)] = r₁(t). + r₂(t) and dt dt dt d dr₂ dr₁ [r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt dt r₁(t) = 3ti + 7t²j +3t³k, r₂(t) = t¹k d 4[r₁(t) · r2(t)] = = dt d dt [r₁(t) = r₂(t)] =