Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such that V₁ V₁ = 35, v₂ · V2 = 334, V3 V3 . . w.v₁ = -105, w. v₂ then w = ·=·0₁ + 0₂ + V3. = 16, 2338, w V3 = 48,

Given a vector begins at (-2, 1) and ends at (3,-4) then the components of the vector are < 4 ¶

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

17) Let a = [3, -4] and b = [−6, k]. a) Determine the value(s) of k such that a + b = a + 6. What is the relationship between the two vectors for this result to be true? b) Determine the value(s) of k such that a + b < a + b. What is the relationship between the two vectors for this result to be true?