2.5 Which of the following sets of vectors are linearly independent?

Prove or disprove ilie following claims: if u, v, and w are linearly independent in vector space V, ilien so are

a) u, u + v, and u + v + w .

b) u + 2v - w , u - 2v - w , and 4v .

c) u-v,v-w,andw-u.

d) -u + v + w , u - v + w , and -u + v - w .

Transcribed Image Text:

a) -9, 3 -2 in the space of real 3-tuples over the field of 1 reals. b) -i {4} in the space of complex pairs over the -i field of reals. 3+4i c) {22 2+2s-1, -2s +2s+s, s-s-5} in the space of polynomials over the field of reals.