Let nu1 3 1 3 1 nu2 1 3 1 3 and nu3 3 1 1 3 Without doing

Let nu_1 = [-3 1 3 -1], nu_2 = [1 -3 -1 3], and nu_3 = [3 -1 -1 3]. Without doing any computation, answer the following questions: a) Do the three vectors {nu_1, nu_2, nu_3} span R^4? Justify your answer. b) Do the three vectors {nu_1, nu_2, nu_3} span R^3? Justify your answer.

Solution

a)

No.

R4 has dimension 4 so needs a minimum of 4 vectors to span R4

b)

No.

Each vector has size 4x1 but vectors in R3 have size: 3x1 hence any vector in span of these three vectors does not lie in R3