Let H span {(0,-1,-2), (-2, -4, 1), (3, 3, -1)}. A basis for the subspace HCR³ is { 2. }. vector

The set containing the elements specified also possesses its relevant operations of multiplication over reals and vector addition. Is the set a real vector space?

Determine a vector that is perpendicular to (2,-5,-1) and (4,0,1).

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

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

isto 5 4 3 2 - 4c = < 1 5 -4 -3 -2 -1 -1 -2 wŃ -3 -4 1 2 3 4 Find the components of the vector -4c based on the vector shown.

The coordinates of the terminal point of the vector with its initial point at (-3, 2) is (a, b). State the value of a + 2b. *

Suppose and are vectors such that a × b = (3, 1, 4). What is the cross product of twice of a with twice of ? (6, 2, 8) (0, 0, 0) (3, 1, 4) (12, 4, 16)

Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, –1, 3), (5, 0, 4)} (a) z = (3, –4, 8) - - ( 4 )a, • ( 1 Z = (») v-(10, -) 1 59 V = 18, 4 1 7 )e, + ( V = 4 (c) w = (3, -9, 15) ( 9 s, + ( -3 W = (d) u = (4, 1, –1) u =