Linear Algebra Find Dimension and basis Find the dimension o

Linear Algebra: Find Dimension and basis

Find the dimension of the vector space V and give a basis for V. (Enter your answers as a comma-separated list.) V = {p(x) in P_2: p{0) = 0} dim V = basis

Solution

General polynomial in P2 is

p(x)=a+bx+cx^2

p(0)=0 gives a=0

p(x)=bx+cx^2

HEnce, it can be spanned by x and x^2

dim V=2

basis ={x,x^2}