CS PA4PA4 N Netflix W calendar Linear Tra O Lecture 30 Line

CS PA4-PA4 N Netflix | W calendar Linear Tra.. O Lecture 30 Linear Inde.. 0 The Span o patrick MT Spring 15 Hom / hw6-sp15 Elementary X ·l® www.math.colostate.edu/~mcarthur/M 369 /spring 201 5 /hw6-sp 15.pdf 2 of 2 - + 250% 9. Show that the set of polynomials of degree less than or equal to 3, P3 such that p(7) = 0 is a subspace of P3. What is it\'s dimension?

Solution

let the set of polynomials of degree less than or equal to 3 , such that P(7) = 0 be U

let p1,p2 belongs to U

=>
p1(7) = 0, p2(7) = 0

In order to prove that U is a subspace, we need to prove that p1 + kp2 also belongs to U for any scalar k

(p1+kp2)(7) = p1(7) + kp2(7) = 0 +k*0 = 0

=>
p1+kp2 also belongs to U

=> U is a subspace

thus proved