Let

{v_(1),v_(2),v_(3),v_(4)}

be a basis for a vector space

V

. Answer the following\ questions and justify your answers.\ (a) Is

{v_(1),v_(1)+v_(2),v_(1)+v_(3),v_(1)+v_(4)}

a basis for

V

?\ (b) Is

{v_(1)+v_(2),v_(1)+v_(3),v_(1)+v_(4)}

a basis for

V

?\ (c) Can you find a vector

uinV

, not equal to

v_(1),v_(2),v_(3)

or

v_(4)

such that\

{u,v_(1),v_(2),v_(3),v_(4)}

is a basis for

V

?

5. Let {v1,v2,v3,v4} be a basis for a vector space V. Answer the following questions and justify your answers. (a) Is {v1,v1+v2,v1+v3,v1+v4} a basis for V ? (b) Is {v1+v2,v1+v3,v1+v4} a basis for V ? (c) Can you find a vector uV, not equal to v1,v2,v3 or v4 such that {u,v1,v2,v3,v4} is a basis for V