7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

Find the vector determined by 18 || = B = {[.]. 9 6 12 3 9 2 -8 " where B = 3 [-]

Define' a vector to contain 2 components: (a,b) where a a rational number, b is an irrational number. Let S? be a set that contains such vectors, ie. s*={ (a,b)| for all rational numbers a, irrational numbers b}. For example, (3.14,71) is in S², but (e,71) is not in S² – 1 & e are well known math constants. Is S a vector space over the integers?

Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3

Find Vector A and B such that A is parallel to <2,1,-1>, B is perpendicular to <2,1,-1> and A + B = <-1,5,7>

PLEASE ANSWER number 1 for me, thank in advnace

Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector 1 Which of the following points (given by their coordinates) lie on | 1? Select one: a. (-3, 1, -1) b. (-2, -1, 0) c. (-3, 2,-1) d. (-4, 3, 0)