Answer Happy

For this section state whether the following statements are True or False. Pro- vide complete justifications for your choice. Each question is 10 points. 11) Let T R¹ kernel of T is atleast 1. R³ be a linear transformation. Then the dimension of 12) Let u be a vector in R2 such that u is orthogonal to e₁ + e2 and e1 - e2, then u has to be the zero vector. Here e, and e2 are elements of the standard basis in R2. 13) Let S be a set of 20 vectors in R20, then S forms a basis of R20 14) Let v₁, 2, 3, 4, 5 are vectors in R6 such that the intersection of the sub- spaces Span(vi, 02, 03) and Span(v4, 5) is the zero vector. Then (vi, U2, U3, V4, V5) U3, U4, 05) is linearly independent. 15) Let A be a 3 x 3 matrix such that v₁ and v2 are vectors which satisfy Av₁ = b and Av2 = b, then 2v1 - 302 € Null(A).