The figure below shows four named points A, B, C, and D on a grid generated by two vectors V₁, V2 in R². Part 1 A = B = C = 03 D= C B V2 Write each point as a sum of scalar multiples of 7₁ and 72. Enter v1 for ₁ and v2 for V₂. v1 A D

Determine whether the vectors are linearly independent. BA -4 -6 2

Let 03 = If possible, express w as a linear combination of the vectors 1, 02 and 3. Otherwise, enter DNE. For example, the answer w = 401+502+603 would be entered 4v1 + 5v2 + 6v3. w =

Determine if b is a linear combination of the other vectors. If so, express b as a linear combination. (If b cannot be written as a linear combination of the other two vectors, enter DNE in both answer blanks.) a = a, = b = Jas + ( 2 b =

a. Write the vector (8, 5, 30) as a linear combination of a₁ = (4, -4,1), d₂ = (4, -5, 5) and d3 = (0, -4,-4). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ +52 + 6ả3, which would be entered as 4a1 + 5a2 + 6a3. (8,5, 30) = b. Represent the vector (8,5,30) in terms of the ordered basis B = {(4,-4, 1), (4, −5, 5), (0, -4,-4)}. Your answer should be a vector of the general form . [(8, 5, 30)] B =