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- Find (a) ker(T) and (b) range(T).T: R3→R3, T(x, y, z) = (x + y, y + z, x − z)A ballet dancer jumps in the air. The height, h(t), in feet, of the dancer at time t, in seconds since the start of the jump, is given byh(t) = −16t^2 + 16Tt,where T is the total time in seconds that the ballet dancer is in the air.(b) When, in terms of T, does the maximum height of the jump occur?(c) Show that the time, T, that the dancer is in the air is related to H, the maximum height of the jump, by the equation H = 4T2An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model p = -t2 + 13t +130, where 1 ≤ t ≤ 6. Find the day the 160 students had the flu. Recall that the restriction on t is at most 6.