Let A 3 Be M = {e; -e; 11 Si

Unit vector in R4.)

(a) Determine the 6 elements of M and show that M is linearly dependent.

(b) M contains three linearly independent vectors. Show this by entering the rank

calculate a suitable matrix.

(c) Let B = (e1,e2, e3, e4) be the canonical basis of R4. Replace three vectors from B

successively by three linearly independent vectors of M, so that one has a basis of

R4, which contains three vectors from M. To do this, use the replacement set

von Steinitz.

(1 + 2 + 2 Points)