Let C₁ (t) esti + 7 sin(t)j + tªk and c₂ (t) = e¯5ti + 3 cos(t)j - 4t¹k. (Enter your solution as a single vector using the vector form (*,*,*). Use symbolic notation and fractions where needed.) d dt = [C₁ (t) + C₂ (t)] =

Let v = (-4, -4, -3) Calculate: vxi = ( vx j = ( vx k = (

Sketch the graph of the vector-valued function r(t) = (2t – 1)² î + (2t +2) ĵ. Draw arrows on your graph to indicate the orientation.

a b Let A = and let k be a scalar. Find a formula that relates det(kA) to k and det(A). c d Find det(A). det(A) = (Simplify your answer.) Find det(kA). det(kA) = | (Simplify your answer.) Use the preceding steps to find a formula for det(kA). Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer.) A. det(kA) = • det(A) + B. det(kA) = + det(A) Oc. det(kA) = |- det(A) O D. det(kA) = • det(A)