Algebra Consider the matrices A= (1 0 2 0 3 4 5 6 0) B= (0 3 4 1 0 2 50 60 0) (a) Using the correspondence between elementary matrices and elementary row operations, find a matrix C such that CA = B. (b) Using the expressions for the inverses of elementary matrices from the lecture notes, and the rule for inverses of products of matrices, find the inverse matrix of C (c) Check your answer by computing directly that C^-B = A. Calculus (a) what is the value of are sin(sin(pi))? Show your reasoning. (b) A ball is dropped from a height of 30 m. If we neglect air resistance and apply Newton's second law, the height of the ball above the ground after t seconds is given by y(t)=30 - y^t^2/2, for t elementof [0, t] where g is the gravitational acceleration, which we take to be 9.8 m/s/s, and t_f > 0 is the time at which the ball hits the ground. Find the inverse function t(y) and use this to determine t_f.