Ais an n\times n matrix. check the true statements below: a. an eigenspace of a is just a null space of a certain matrix. b. if v_{1} and v_{2} are linearly independent eigenvectors, then they correspond to distinct eigenvalues. c. if ax = \lambda x for some nonzero vector x, then \lambda is an eigenvalue of a. d. if ax = \lambda x for some vector x, then x is an eigenvector of a. e. the eigenvalues of a matrix are on its main diagonal.

(8%) problem 12. a bowling ball of mass mb 3 kg 's rolled down the lane with a velocity ofy-2/ m s lt strikes a single remaining pin mp 0.93 kg head on. after the collision the bowling ball has a velocity (in the same direction) of v2 1.1 m/s. = ▲ 33% part (a) write an expression for the velocity of pin in the horizontal direction after the impact, im ,, 33% part (b) what is the pins speed in ms? 33% part (c) assuming the coefficient of friction s μ,-0.1. how far in meters could the pin slide before stopping if it doesn't topple?