Let v1=( 0 1 -1 2)^T v2=(1 0 -2 1)^T Let V=Span{v1,v2} Find a basis for the orthogonal complement of V.

If Span {u,v} = R^2 then {2u,u+v} is a basis for R^2.   Is this statement true?

Does the ordered set v, v, va form a basis for R^3? If not, which vectors would you subtract from the set and which standard basis vector can you add to the set to make it a basis for R^3? vi = (1,–1, –2) = (5, –4, –7) v = (-3, 1,0) Select all answers that are correct. O subtract vector v 1 from the set O no it does not form a basis for R^3 O subtract vector v_3 from the set O yes it forms a basis for R^3 O add vector e_1 O add vector e 2 subtract vector v_2 from the set O add vector e_3

Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. - 2 6 -2 - 6 105 5 A = 2 -9 - 2 4 B = 0 3 4 2 - 3 12 1 -7 0 0 0 0 A column vector basis for Nul A is }. (Use a comma to separate vectors as needed.)