Let S p x E P p 1 p 2 a Show that S is a subspace of P b Find a basis and the dimension of S c Find the coordinates of the vector p x 5x 15x 7 relative to the basis found part b 0 Determine whether the following statement is true or false Justify your answer with a proof or a counterexample a The planes x y 2z 5 and x y z 1 2 3 1 1 2 s 3 0 7 t are perpendicular b If A is a matrix such that A is symmetric then A is symmetric c If u v w is a basis of a vector space V then u u v w u 2v 2w is also a basis of V
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