(20 points) - Section 3.1\ a. Given the polynomials

vec(p)=-5+2x+x^(2)

and

vec(q)=3+2x-4x^(2)

\ i. find the standard inner product on

P_(2)

of the given polynomials.\ ii. find

||vec(p)||

and

d(vec(p),vec(q))

relative to the standard inner product on

P_(2)

.\ b. Given the matrices\

U=[[1,2],[-3,5]],V=[[4,6],[0,8]]

\ i. compute the standard inner product on

M_(22)

of the given matrices.\ ii. find

||U||

and

d(U,V)

relative to the standard inner product on

M_(z2)

.

a. Given the polynomials p=5+2x+x2 and q=3+2x4x2 i. find the standard inner product on P2 of the given polynomials. ii. find p and d(p,q) relative to the standard inner product on P2. b. Given the matrices U=[1325],V=[4068] i. compute the standard inner product on M22 of the given matrices. ii. find U and d(U,V) relative to the standard inner product on Mz2