Which of the following statements are true? I: 2v, +2v2 - 3v3 is an affine combination of the 3 vectors. I: III: The affine hull of two distinct points is a plane. If S= {x}, then aff S = {x}. IV: If a set of vectors in R" is linearly independent, then every vector in R" can be written as an affine combination of these vectors. O A. I and l| O B. I, III, and IV O C. I and III O D. Il and IV

Find the dot product of each pair of the given vectors. -6 [13 21-₂2-| 1 |-√₂- 4 2 V₁ V2 V₁ V3 V2 V3 V₁ 2 Determine if the given vectors form an orthogonal set. o These vectors form an orthogonal set. These vectors do not form an orthogonal set.

Let v₁ = 0 0 -3 O 0 - 3 6 and V3 Choose the correct answer below. 3 -4 -9 Does (V₁ V₂ V3} span R³? Why or why not? A. No. The set of given vectors spans a plane in R³. Any of the three vectors can be written as a linear combination of the other two. B. Yes. Any vector in R³ except the zero vector can be written as a linear combination of these three vectors. C. Yes. When the given vectors are written as the columns of a matrix A, A has a pivot position in every row. D. No. When the given vectors are written as the columns of a matrix A, A has a pivot position in only two rows. wrth g

Please solve this linear algebra problem with a good explanation.

Let a₁ = 1 - 1 a₂ = The value(s) of h is(are) -6 - 25 2 5 11- h and b = LO For what value(s) of h is b in the plane spanned by a, and a₂? (Use a comma to separate answers as needed.)

Let u4 be a linear combination of {u₁, U2, U3}. Select the best statement. ● A. {u₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U2, U3} is the zero vector. ● B. {U1, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U1, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U1, U2, U3, u4} is always a linearly dependent set of vectors. ● E. {U1, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. ● F. none of the above