4.1 Exercises\ Let

V

be the first quadrant in the

xy

-plane; that is, let\

V={[[x],[y]]:x>=0,y>=0}

\ a. If

u

and

v

are in

V

, is

u+v

in

V

? Why?\ b. Find a specific vector

u

in

V

and a specific scalar

c

such\ that

cu

is not in

V

. (This is enough to show that

V

is not\ a vector space.)\ Let

W

be the union of the first and third quadrants in the

xy

-\ plane. That is, let

W={[[x],[y]]:xy>=0}

.\ a. If

u

is in

W

and

c

is any scalar, is

cu

in

W

? Why?\ b. Find specific vectors

u

and

v

in

W

such that

u+v

is not\ in

W

. (This is enough to show that

W

is not a vector\ space.)\ All polynomials of degree\ cients.\ All polynomials in

P_(n)

su\ Let

H

be the set of al\ vector

v

in

R^(3)

such th\ that

H

is a subspace\ Let

H

be the set of\

H

is a subspace of

4.1 Exercises 1. Let V be the first quadrant in the xy-plane; that is, let V={[xy]:x0,y0} a. If u and v are in V, is u+v in V ? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. (This is enough to show that V is not a vector space.) 2. Let W be the union of the first and third quadrants in the xy plane. That is, let W={[xy]:xy0}. a. If u is in W and c is any scalar, is cu in W ? Why? b. Find specific vectors u and v in W such that u+v is not in W. (This is enough to show that W is not a vector space.) 7. All polynomials of degree cients. 8. All polynomials in Pn su 9. Let H be the set of al vector v in R3 such th that H is a subspace ' 10. Let H be the set of : H is a subspace of