linear algebra question MC 18 Let W be the vector space of a

linear algebra question

MC 18. Let W be the vector space of all polynomials p(t) of degree up to 3 with the property that p(7) 0. What is the dimension of W? (a) 1 (b) 2 (c) 3 (d) 4 (e) W is not a vector space.

Solution

p(t)=at³+bt²+ct+d hence p(7)=343a+49b +7c+d=0 where abc&d are scalors. ANS The Dimention ofW will be (d)