Consider the following vectors: 1 ·1 3 a =-2 -3 b= = = 0 -8 -3 For each of the following vectors, determine whether it can be written as a linear combination of these vectors. If so, give the linear combination using the vector names above. 8 V1= 1 < Select an answer > 0 -3 V2=9 < Select an answer > 0 2 V3= II < Select an answer >

a⃗ =⟨−3,−2⟩ and b⃗ =⟨2,4⟩​. Represent a⃗ −b⃗  using the head-to-tail method. Use the Vector tool to draw the vectors, complete the subtraction by the head-to-tail method, and draw a⃗ −b⃗ .

Find the sum and difference of the following vectors:     a. <-4,6>+<5,0> b. <-7,5>0<-5,-9>

a⃗ =⟨5, −1⟩ and b⃗ =⟨−2,−2⟩. Represent a⃗ +b⃗  using the head to tail method. Use the Vector tool to draw a⃗  and b⃗ , complete the head to tail method, and draw a⃗ +b⃗ .

Given the vectors a=(7, -4) and b=(-3, 8), find 2a and a +b. Write your answers in component form. 2a = a + b =

Evaluate the following vector expression: a = [3 -6 -2] -3 Calculate 3(ax + az) and enter your answer in the answer box below

Determine which of the following vectors are orthogonal to each other: 12 2 X = -5 3 X2 = |1 X3 = |-3 3

Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b = help (vectors)

a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =

Given the vectors m= (9, − 1) and n=(8, 6), find 5m and m+n. Write your answers in component form.