Let H = span {V₁, V2, V3, V4}. For each of the following sets of vectors determine whether H is a line, plane, or R³. Select an Answer 2 -8-8-8-8 -1 Select an Answer V 2. -3 -2 Select an Answer V 1. 3 6 -0-0-0-0 -1 -1 2 3. -1 -2 9 -2 4 -7 -8-8-8-8 5 7 -5 6 24 16 -5 1

For which a are the vectors ⟨2,a,1⟩ and ⟨1,−2,4⟩ perpendicular?

Determine whether the set of vectors is orthogonal. [-10] 10] [-10] -20 0 10 -10 -10 Select one: O A. Yes O B. No -10

1 -4 5. List 5 vectors in the span of and -2 1 3.

Express the indicated vector w as a linear combination of the given vectors v₁ and v₂ if this is possible. If not, show that it is impossible. W = -7 - 9 - 2 3 5 8 -4 - 3 Select the correct answer below, and fill in the answer box(es) to complete your choice. ) v₁ + ( ) v₂. A. It is possible to express the vector w in terms of v₁ and v₂, as w= (Type integers or fractions.) B. It is impossible to express the vector w in terms of V₁ and V₂, because an echelon form of the augmented matrix [V₁ V₂ W], E= (Type an integer or simplified fraction for each matrix element.) shows that the system is inconsistent.

Express the indicated vector w as a linear combination of the given vectors v1 and v2 if this is possible. If​ not, show that it is impossible. w= (-1,0,7), V1= (7,6,5), v2=(6,5,3) Select the correct answer​ below, and fill in the answer​box(es) to complete your choice. A.It is possible to express the vector w in terms of v1 and v2​, as w=(___)v1+(___)v2. ​(Type integers or​ fractions.) B.It is impossible to express the vector w in terms of v1 and v2​, because an echelon form of the augmented matrix [v1  v2  w]​, E=___?​, shows that the system is inconsistent.