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

Find a basis of Span((1,-1,3,0), (2, 1, -2, -1), (3, 3, -7,-2)).

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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{ (1,2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii) Determine whether the vector (1,2, 6) is a linear combination of the vectors (1, 2, – 1), (3, 1, 1), and (-4, 0, 6). (Include all the steps in your reasoning.).

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.

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 =

Find a basis of the subspace of R* consisting of all vectors of the form X1 -8x1 + x2 -6х — 2х2 -бх — 4x2 swer should be a list of row vectors separated by commas. (Click vector to learn about entering { }.

Determine the following three vectors {<2,1,0>, <4,2,2>, <-2,-1,3>} forms a basis for R^3. Expalain your answer.

Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the vectors (6,5) and (7,4). (Give your answer in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) T(u, v) = (6u+7v,5u +4v) Calculate the double integral of e2x-over P via change of variables. (Express numbers in exact form. Use symbolic notation and fractions where needed.) 1/₂ 2²x-A= Incorrect 10 ½ (e¹⁰ − 1)(e² - 1) 70 CA